Proceedings of the Edinburgh Mathematical Society最新文献

{"title":"The Schwarzian norm estimates for Janowski convex functions","authors":"Md Firoz Ali, Sanjit Pal","doi":"10.1017/s0013091524000014","DOIUrl":"https://doi.org/10.1017/s0013091524000014","url":null,"abstract":"For <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091524000014_inline1.png\" /> <jats:tex-math>$-1leq B lt Aleq 1$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091524000014_inline2.png\" /> <jats:tex-math>$mathcal{C}(A,B)$</jats:tex-math> </jats:alternatives> </jats:inline-formula> denote the class of normalized Janowski convex functions defined in the unit disk <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091524000014_inline3.png\" /> <jats:tex-math>$mathbb{D}:={zinmathbb{C}:|z| lt 1}$</jats:tex-math> </jats:alternatives> </jats:inline-formula> that satisfy the subordination relation <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091524000014_inline4.png\" /> <jats:tex-math>$1+zf''(z)/f'(z)prec (1+Az)/(1+Bz)$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. In the present article, we determine the sharp estimate of the Schwarzian norm for functions in the class <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091524000014_inline5.png\" /> <jats:tex-math>$mathcal{C}(A,B)$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The Dieudonné’s lemma which gives the exact region of variability for derivatives at a point of bounded functions, plays the key role in this study, and we also use this lemma to construct the extremal functions for the sharpness by a new method.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"39 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139773202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Estimating the Hausdorff measure using recurrence","authors":"Łukasz Pawelec","doi":"10.1017/s0013091523000755","DOIUrl":"https://doi.org/10.1017/s0013091523000755","url":null,"abstract":"We show a new method of estimating the Hausdorff measure of a set from below. The method requires computing the subsequent closest return times of a point to itself.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139459729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Commutants and complex symmetry of finite Blaschke product multiplication operator in","authors":"Arup Chattopadhyay, Soma Das","doi":"10.1017/s0013091523000809","DOIUrl":"https://doi.org/10.1017/s0013091523000809","url":null,"abstract":"<p>Consider the multiplication operator <span>M<span>B</span></span> in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110124038844-0402:S0013091523000809:S0013091523000809_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$L^2(mathbb{T})$</span></span></img></span></span>, where the symbol <span>B</span> is a finite Blaschke product. In this article, we characterize the commutant of <span>M<span>B</span></span> in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110124038844-0402:S0013091523000809:S0013091523000809_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$L^2(mathbb{T})$</span></span></img></span></span>. As an application of this characterization result, we explicitly determine the class of conjugations commuting with <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110124038844-0402:S0013091523000809:S0013091523000809_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$M_{z^2}$</span></span></img></span></span> or making <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110124038844-0402:S0013091523000809:S0013091523000809_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$M_{z^2}$</span></span></img></span></span> complex symmetric by introducing a new class of conjugations in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110124038844-0402:S0013091523000809:S0013091523000809_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$L^2(mathbb{T})$</span></span></img></span></span>. Moreover, we analyse their properties while keeping the whole Hardy space, model space and Beurling-type subspaces invariant. Furthermore, we extended our study concerning conjugations in the case of finite Blaschke products.</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139423344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multidimensional Frank–Laptev–Weidl improvement of the Hardy inequality","authors":"Prasun Roychowdhury, Michael Ruzhansky, Durvudkhan Suragan","doi":"10.1017/s0013091523000780","DOIUrl":"https://doi.org/10.1017/s0013091523000780","url":null,"abstract":"<p>We establish a new improvement of the classical <span>L<span>p</span></span>-Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new kind of development of the one-dimensional Hardy inequality. Using some radialisation techniques of functions and then exploiting symmetric decreasing rearrangement arguments on the real line, the new multidimensional version of the Hardy inequality is given. Some consequences are also discussed.</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139423404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Goldie dimension for C*-algebras","authors":"Mohammad Rouzbehani, Massoud Amini, Mohammad B. Asadi","doi":"10.1017/s0013091523000767","DOIUrl":"https://doi.org/10.1017/s0013091523000767","url":null,"abstract":"<p>In this article, we introduce and study the notion of Goldie dimension for C*-algebras. We prove that a C*-algebra <span>A</span> has Goldie dimension <span>n</span> if and only if the dimension of the center of its local multiplier algebra is <span>n</span>. In this case, <span>A</span> has finite-dimensional center and its primitive spectrum is extremally disconnected. If moreover, A is extending, we show that it decomposes into a direct sum of <span>n</span> prime C*-algebras. In particular, every stably finite, exact C*-algebra with Goldie dimension, that has the projection property and a strictly full element, admits a full projection and a non-zero densely defined lower semi-continuous trace. Finally we show that certain C*-algebras with Goldie dimension (not necessarily simple, separable or nuclear) are classifiable by the Elliott invariant.</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"16 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Infinitesimally Moebius bendable hypersurfaces","authors":"M.I. Jimenez, R. Tojeiro","doi":"10.1017/s0013091523000792","DOIUrl":"https://doi.org/10.1017/s0013091523000792","url":null,"abstract":"&lt;p&gt;Li, Ma and Wang have provided in [13] a partial classification of the so-called Moebius deformable hypersurfaces, that is, the umbilic-free Euclidean hypersurfaces &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110125208839-0507:S0013091523000792:S0013091523000792_inline1.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$fcolon M^nto mathbb{R}^{n+1}$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; that admit non-trivial deformations preserving the Moebius metric. For &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110125208839-0507:S0013091523000792:S0013091523000792_inline2.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$ngeq 5$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;, the classification was completed by the authors in [12]. In this article we obtain an infinitesimal version of that classification. Namely, we introduce the notion of an infinitesimal Moebius variation of an umbilic-free immersion &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110125208839-0507:S0013091523000792:S0013091523000792_inline3.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$fcolon M^nto mathbb{R}^m$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; into Euclidean space as a one-parameter family of immersions &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110125208839-0507:S0013091523000792:S0013091523000792_inline4.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$f_tcolon M^nto mathbb{R}^m$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;, with &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110125208839-0507:S0013091523000792:S0013091523000792_inline5.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$tin (-epsilon, epsilon)$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; and &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110125208839-0507:S0013091523000792:S0013091523000792_inline6.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$f_0=f$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;, such that the Moebius metrics determined by &lt;span&gt;f&lt;span&gt;t&lt;/span&gt;&lt;/span&gt; coincide up to the first order. Then we characterize isometric immersions &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110125208839-0507:S0013091523000792:S0013091523000792_inline7.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$fcolon M^nto mathbb{R}^m$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; of arbitrary codimension that admit a non-trivial infinitesimal Moebius variation among those that admit a non-trivial conformal infinitesimal variation, and use such characterization to classify the u","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"9 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On traces of Bochner representable operators on the space of bounded measurable functions","authors":"Marian Nowak, Juliusz Stochmal","doi":"10.1017/s0013091523000779","DOIUrl":"https://doi.org/10.1017/s0013091523000779","url":null,"abstract":"<p>Let Σ be a <span>σ</span>-algebra of subsets of a set Ω and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110130638066-0304:S0013091523000779:S0013091523000779_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$B(Sigma)$</span></span></img></span></span> be the Banach space of all bounded Σ-measurable scalar functions on Ω. Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110130638066-0304:S0013091523000779:S0013091523000779_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$tau(B(Sigma),ca(Sigma))$</span></span></img></span></span> denote the natural Mackey topology on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110130638066-0304:S0013091523000779:S0013091523000779_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$B(Sigma)$</span></span></img></span></span>. It is shown that a linear operator <span>T</span> from <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110130638066-0304:S0013091523000779:S0013091523000779_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$B(Sigma)$</span></span></img></span></span> to a Banach space <span>E</span> is Bochner representable if and only if <span>T</span> is a nuclear operator between the locally convex space <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110130638066-0304:S0013091523000779:S0013091523000779_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$(B(Sigma),tau(B(Sigma),ca(Sigma)))$</span></span></img></span></span> and the Banach space <span>E</span>. We derive a formula for the trace of a Bochner representable operator <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110130638066-0304:S0013091523000779:S0013091523000779_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$T:B({cal B} o)rightarrow B({cal B} o)$</span></span></img></span></span> generated by a function <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240110130638066-0304:S0013091523000779:S0013091523000779_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$fin L^1({cal B} o, C(Omega))$</span></span></img></span></span>, where Ω is a compact Hausdorff space.</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"9 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The spherical growth series of Dyer groups","authors":"Luis Paris, Olga Varghese","doi":"10.1017/s0013091523000743","DOIUrl":"https://doi.org/10.1017/s0013091523000743","url":null,"abstract":"<p>Graph products of cyclic groups and Coxeter groups are two families of groups that are defined by labelled graphs. The family of Dyer groups contains these both families and gives us a framework to study these groups in a unified way. This paper focuses on the spherical growth series of a Dyer group <span>D</span> with respect to the standard generating set. We give a recursive formula for the spherical growth series of <span>D</span> in terms of the spherical growth series of standard parabolic subgroups. As an application we obtain the rationality of the spherical growth series of a Dyer group. Furthermore, we show that the spherical growth series of <span>D</span> is closely related to the Euler characteristic of <span>D</span>.</p>","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"79 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138825072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Isomorphisms of quadratic quasigroups","authors":"Aleš Drápal, Ian M. Wanless","doi":"10.1017/s0013091523000585","DOIUrl":"https://doi.org/10.1017/s0013091523000585","url":null,"abstract":"Let &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091523000585_inline1.png\" /&gt; &lt;jats:tex-math&gt;$mathbb F$&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; be a finite field of odd order and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091523000585_inline2.png\" /&gt; &lt;jats:tex-math&gt;$a,binmathbb Fsetminus{0,1}$&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; be such that &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091523000585_inline3.png\" /&gt; &lt;jats:tex-math&gt;$chi(a) = chi(b)$&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091523000585_inline4.png\" /&gt; &lt;jats:tex-math&gt;$chi(1-a)=chi(1-b)$&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, where &lt;jats:italic&gt;χ&lt;/jats:italic&gt; is the extended quadratic character on &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091523000585_inline5.png\" /&gt; &lt;jats:tex-math&gt;$mathbb F$&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;. Let &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091523000585_inline6.png\" /&gt; &lt;jats:tex-math&gt;$Q_{a,b}$&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; be the quasigroup over &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091523000585_inline7.png\" /&gt; &lt;jats:tex-math&gt;$mathbb F$&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; defined by &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091523000585_inline8.png\" /&gt; &lt;jats:tex-math&gt;$(x,y)mapsto x+a(y-x)$&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; if &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091523000585_inline9.png\" /&gt; &lt;jats:tex-math&gt;$chi(y-x) geqslant 0$&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091523000585_inline10.png\" /&gt; &lt;jats:tex-math&gt;$(x,y) mapsto x+b(y-x)$&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; if &lt;jats:inl","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"34 11-12","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138512911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the representability of actions of Leibniz algebras and Poisson algebras","authors":"Alan S. Cigoli, Manuel Mancini, Giuseppe Metere","doi":"10.1017/s0013091523000548","DOIUrl":"https://doi.org/10.1017/s0013091523000548","url":null,"abstract":"In a recent paper, motivated by the study of central extensions of associative algebras, George Janelidze introduces the notion of weakly action representable category. In this paper, we show that the category of Leibniz algebras is weakly action representable and we characterize the class of acting morphisms. Moreover, we study the representability of actions of the category of Poisson algebras and we prove that the subvariety of commutative Poisson algebras is not weakly action representable.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138542301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}