Glasgow Mathematical Journal最新文献

{"title":"Autocorrelations of characteristic polynomials for the Alternative Circular Unitary Ensemble","authors":"Brad Rodgers, Harshith Sai Vallabhaneni","doi":"10.1017/s0017089523000332","DOIUrl":"https://doi.org/10.1017/s0017089523000332","url":null,"abstract":"Abstract We find closed formulas for arbitrarily high mixed moments of characteristic polynomials of the Alternative Circular Unitary Ensemble, as well as closed formulas for the averages of ratios of characteristic polynomials in this ensemble. A comparison is made to analogous results for the Circular Unitary Ensemble. Both moments and ratios are studied via symmetric function theory and a general formula of Borodin-Olshanski-Strahov.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136262656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Representatives of similarity classes of matrices over PIDs corresponding to ideal classes","authors":"Lucy Knight, Alexander Stasinski","doi":"10.1017/s0017089523000356","DOIUrl":"https://doi.org/10.1017/s0017089523000356","url":null,"abstract":"Abstract For a principal ideal domain $A$ , the Latimer–MacDuffee correspondence sets up a bijection between the similarity classes of matrices in $textrm{M}_{n}(A)$ with irreducible characteristic polynomial $f(x)$ and the ideal classes of the order $A[x]/(f(x))$ . We prove that when $A[x]/(f(x))$ is maximal (i.e. integrally closed, i.e. a Dedekind domain), then every similarity class contains a representative that is, in a sense, close to being a companion matrix. The first step in the proof is to show that any similarity class corresponding to an ideal (not necessarily prime) of degree one contains a representative of the desired form. The second step is a previously unpublished result due to Lenstra that implies that when $A[x]/(f(x))$ is maximal, every ideal class contains an ideal of degree one.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135884999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Helfrich functional for compact surfaces in","authors":"Zhongwei Yao","doi":"10.1017/s0017089523000320","DOIUrl":"https://doi.org/10.1017/s0017089523000320","url":null,"abstract":"<p>Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$f;:; Mrightarrow mathbb{C}P^{2}$</span></span></img></span></span> be an isometric immersion of a compact surface in the complex projective plane <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb{C}P^{2}$</span></span></img></span></span>. In this paper, we consider the Helfrich-type functional <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal{H}_{lambda _{1},lambda _{2}}(f)=int _{M}(|H|^{2}+lambda _{1}+lambda _{2} C^{2})textrm{d} M$</span></span></img></span></span>, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$lambda _{1}, lambda _{2}in mathbb{R}$</span></span></img></span></span> with <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$lambda _{1}geqslant 0$</span></span></img></span></span>, <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$H$</span></span></img></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$C$</span></span></img></span></span> are respectively the mean curvature vector and the Kähler function of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline9.png\"><span data-mathjax-type=\"texmath\"><span>$M$</span></span></img></span></span> in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline10.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb{C}P^{2}$</span></span></img></span></span>. The critic","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Null hypersurfaces in 4-manifolds endowed with a product structure","authors":"Nikos Georgiou","doi":"10.1017/s0017089523000319","DOIUrl":"https://doi.org/10.1017/s0017089523000319","url":null,"abstract":"Abstract In a 4-manifold, the composition of a Riemannian Einstein metric with an almost paracomplex structure that is isometric and parallel defines a neutral metric that is conformally flat and scalar flat. In this paper, we study hypersurfaces that are null with respect to this neutral metric, and in particular we study their geometric properties with respect to the Einstein metric. Firstly, we show that all totally geodesic null hypersurfaces are scalar flat and their existence implies that the Einstein metric in the ambient manifold must be Ricci-flat. Then, we find a necessary condition for the existence of null hypersurface with equal nontrivial principal curvatures, and finally, we give a necessary condition on the ambient scalar curvature, for the existence of null (non-minimal) hypersurfaces that are of constant mean curvature.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mutating signed -exceptional sequences","authors":"Aslak Bakke Buan, Bethany Rose Marsh","doi":"10.1017/s0017089523000241","DOIUrl":"https://doi.org/10.1017/s0017089523000241","url":null,"abstract":"Abstract We establish some properties of $tau$ -exceptional sequences for finite-dimensional algebras. In an earlier paper, we established a bijection between the set of ordered support $tau$ -tilting modules and the set of complete signed $tau$ -exceptional sequences. We describe the action of the symmetric group on the latter induced by its natural action on the former. Similarly, we describe the effect on a $tau$ -exceptional sequence obtained by mutating the corresponding ordered support $tau$ -tilting module via a construction of Adachi-Iyama-Reiten.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135687490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum symmetries of Cayley graphs of abelian groups","authors":"Daniel Gromada","doi":"10.1017/s0017089523000198","DOIUrl":"https://doi.org/10.1017/s0017089523000198","url":null,"abstract":"Abstract We study Cayley graphs of abelian groups from the perspective of quantum symmetries. We develop a general strategy for determining the quantum automorphism groups of such graphs. Applying this procedure, we find the quantum symmetries of the halved cube graph, the folded cube graph, and the Hamming graphs.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135637919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"GMJ volume 65 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s0017089523000307","DOIUrl":"https://doi.org/10.1017/s0017089523000307","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135687491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"GMJ volume 65 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s0017089523000290","DOIUrl":"https://doi.org/10.1017/s0017089523000290","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135687492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Relative Dehn functions, hyperbolically embedded subgroups and combination theorems","authors":"H. Bigdely, Eduardo Martínez-Pedroza","doi":"10.1017/s0017089523000265","DOIUrl":"https://doi.org/10.1017/s0017089523000265","url":null,"abstract":"\u0000\t <jats:p>Consider the following classes of pairs consisting of a group and a finite collection of subgroups:<jats:list list-type=\"bullet\">\u0000\t <jats:list-item>\u0000\t\t<jats:label>•</jats:label>\u0000\t\t<jats:p>\u0000\t\t <jats:inline-formula>\u0000\t\t <jats:alternatives>\u0000\t\t <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline1.png\" />\u0000\t\t <jats:tex-math>\u0000$ mathcal{C}= left { (G,mathcal{H}) mid text{$mathcal{H}$ is hyperbolically embedded in $G$} right }$\u0000</jats:tex-math>\u0000\t\t </jats:alternatives>\u0000\t\t </jats:inline-formula>\u0000\t\t</jats:p>\u0000\t </jats:list-item>\u0000\t <jats:list-item>\u0000\t\t<jats:label>•</jats:label>\u0000\t\t<jats:p>\u0000\t\t <jats:inline-formula>\u0000\t\t <jats:alternatives>\u0000\t\t <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline2.png\" />\u0000\t\t <jats:tex-math>\u0000$ mathcal{D}= left { (G,mathcal{H}) mid text{the relative Dehn function of $(G,mathcal{H})$ is well-defined} right } .$\u0000</jats:tex-math>\u0000\t\t </jats:alternatives>\u0000\t\t </jats:inline-formula>\u0000\t\t</jats:p>\u0000\t </jats:list-item>\u0000\t </jats:list></jats:p>\u0000\t <jats:p>Let <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline3.png\" />\u0000\t\t<jats:tex-math>\u0000$G$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> be a group that splits as a finite graph of groups such that each vertex group <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline4.png\" />\u0000\t\t<jats:tex-math>\u0000$G_v$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> is assigned a finite collection of subgroups <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline5.png\" />\u0000\t\t<jats:tex-math>\u0000$mathcal{H}_v$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>, and each edge group <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline6.png\" />\u0000\t\t<jats:tex-math>\u0000$G_e$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> is conjugate to a subgroup of some <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline7.png\" />\u0000\t\t<jats:tex-math>\u0000$Hin mathcal{H}_v$\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> if <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0017089523000265_inline8.png\" />\u0000\t\t<jats:tex-math>\u0000$e$\u0000</jats:tex-math>\u0000\t </jats:alt","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47620609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the structure of lower bounded HNN extensions","authors":"Paul Bennett, T. Jajcayová","doi":"10.1017/S001708952300023X","DOIUrl":"https://doi.org/10.1017/S001708952300023X","url":null,"abstract":"Abstract This paper studies the structure and preservational properties of lower bounded HNN extensions of inverse semigroups, as introduced by Jajcayová. We show that if \u0000$S^* = [ S;; U_1,U_2;; phi ]$\u0000 is a lower bounded HNN extension then the maximal subgroups of \u0000$S^*$\u0000 may be described using Bass-Serre theory, as the fundamental groups of certain graphs of groups defined from the \u0000$mathcal{D}$\u0000 -classes of \u0000$S$\u0000 , \u0000$U_1$\u0000 and \u0000$U_2$\u0000 . We then obtain a number of results concerning when inverse semigroup properties are preserved under the HNN extension construction. The properties considered are completely semisimpleness, having finite \u0000$mathcal{R}$\u0000 -classes, residual finiteness, being \u0000$E$\u0000 -unitary, and \u0000$0$\u0000 - \u0000$E$\u0000 -unitary. Examples are given, such as an HNN extension of a polycylic inverse monoid.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46064272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}