Journal of Pure and Applied Algebra最新文献

{"title":"Algebraically universal categories of relational structures","authors":"Ioannis Eleftheriadis","doi":"10.1016/j.jpaa.2025.107984","DOIUrl":"10.1016/j.jpaa.2025.107984","url":null,"abstract":"<div><div>We study the problem of representability of categories of algebras in categories of relational structures. This is a general framework for a long line of research pertaining to the realisation of algebraic structures in graphs. Drawing inspiration from a combinatorial property of classes of finite graphs known as nowhere density that originates from the work of Nešetřil and Ossona de Mendez, we establish a partial characterisation of those relational categories which are algebraically universal, meaning that they fully embed all categories of algebras. More precisely, we show that the any algebraically universal category of relational structures must necessarily contain subdivided complete graphs of any infinite size. Conversely, we establish that any relational category closed under removal of relations and having this property may be oriented to obtain an algebraically universal category. For the proof of the above, we develop a categorical framework for relational gadget constructions. This generalises existing work on algebraic representability in categories of finite graphs to categories of relational structures of unbounded size.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107984"},"PeriodicalIF":0.7,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143906212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Orthogonal involutions over fields with I3=0","authors":"Karim Johannes Becher ,&nbsp;Fatma Kader Bingöl","doi":"10.1016/j.jpaa.2025.107979","DOIUrl":"10.1016/j.jpaa.2025.107979","url":null,"abstract":"<div><div>We provide upper bounds on the <em>u</em>-invariant for skew-hermitian forms over a quaternion algebra with its canonical involution in terms of the <em>u</em>-invariant of the base field <em>F</em> of characteristic different from 2 when <span><math><msup><mrow><mi>I</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>F</mi><mo>=</mo><mn>0</mn></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107979"},"PeriodicalIF":0.7,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143906189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Central H-spaces and banded types","authors":"Ulrik Buchholtz ,&nbsp;J. Daniel Christensen ,&nbsp;Jarl G. Taxerås Flaten ,&nbsp;Egbert Rijke","doi":"10.1016/j.jpaa.2025.107963","DOIUrl":"10.1016/j.jpaa.2025.107963","url":null,"abstract":"<div><div>We introduce and study <em>central</em> types, which are generalizations of Eilenberg–Mac Lane spaces. A type is central when it is equivalent to the component of the identity among its own self-equivalences. From centrality alone we construct an infinite delooping in terms of a tensor product of <em>banded types</em>, which are the appropriate notion of torsor for a central type. Our constructions are carried out in homotopy type theory, and therefore hold in any ∞-topos. Even when interpreted into the ∞-topos of spaces, our approach to constructing these deloopings is new.</div><div>Along the way, we further develop the theory of H-spaces in homotopy type theory, including their relation to <em>evaluation fibrations</em> and Whitehead products. These considerations let us, for example, rule out the existence of H-space structures on the 2<em>n</em>-sphere for <span><math><mi>n</mi><mo>&gt;</mo><mn>0</mn></math></span>. We also give a novel description of the moduli space of H-space structures on an H-space. Using this description, we generalize a formula of Arkowitz–Curjel and Copeland for counting the number of path components of this moduli space. As an application, we deduce that the moduli space of H-space structures on the 3-sphere is <span><math><msup><mrow><mi>Ω</mi></mrow><mrow><mn>6</mn></mrow></msup><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107963"},"PeriodicalIF":0.7,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143865158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparison of Frobenius algebra structures on Calabi–Yau toric hypersurfaces","authors":"Jeehoon Park ,&nbsp;Philsang Yoo","doi":"10.1016/j.jpaa.2025.107973","DOIUrl":"10.1016/j.jpaa.2025.107973","url":null,"abstract":"<div><div>We establish an isomorphism between two Frobenius algebra structures, termed CY and LG, on the primitive cohomology of a smooth Calabi–Yau hypersurface in a simplicial Gorenstein toric Fano variety. As an application of our comparison isomorphism, we observe the existence of a Frobenius manifold structure on a finite-dimensional subalgebra of the Jacobian algebra of a homogeneous polynomial which may exhibit a non-compact singularity locus.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107973"},"PeriodicalIF":0.7,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Idoneal genera and K3 surfaces covering an Enriques surface","authors":"Simon Brandhorst ,&nbsp;Serkan Sonel ,&nbsp;Davide Cesare Veniani","doi":"10.1016/j.jpaa.2025.107974","DOIUrl":"10.1016/j.jpaa.2025.107974","url":null,"abstract":"<div><div>We introduce the notion of idoneal genera, which are a generalization of Euler's idoneal numbers. We prove that there exist only a finite number of idoneal genera, and we provide an algorithm to enumerate all idoneal genera of rank at least 3. As an application, we classify transcendental lattices of K3 surfaces covering an Enriques surface.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107974"},"PeriodicalIF":0.7,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Compact groups in which commutators have finite right Engel sinks","authors":"Evgeny Khukhro ,&nbsp;Pavel Shumyatsky","doi":"10.1016/j.jpaa.2025.107970","DOIUrl":"10.1016/j.jpaa.2025.107970","url":null,"abstract":"<div><div>A right Engel sink of an element <em>g</em> of a group <em>G</em> is a subset containing all sufficiently long commutators <span><math><mo>[</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>[</mo><mo>[</mo><mi>g</mi><mo>,</mo><mi>x</mi><mo>]</mo><mo>,</mo><mi>x</mi><mo>]</mo><mo>,</mo><mo>…</mo><mo>,</mo><mi>x</mi><mo>]</mo></math></span>. We prove that if <em>G</em> is a compact group in which, for some <em>k</em>, every commutator <span><math><mo>[</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>[</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>]</mo></math></span> has a finite right Engel sink, then <em>G</em> has a locally nilpotent open subgroup. If in addition, for some positive integer <em>m</em>, every commutator <span><math><mo>[</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>[</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>]</mo></math></span> has a right Engel sink of cardinality at most <em>m</em>, then <em>G</em> has a locally nilpotent subgroup of finite index bounded in terms of <em>m</em> only.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107970"},"PeriodicalIF":0.7,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite groups with few character values that are not character degrees","authors":"Sesuai Y. Madanha ,&nbsp;Xavier Mbaale ,&nbsp;Tendai M. Mudziiri Shumba","doi":"10.1016/j.jpaa.2025.107969","DOIUrl":"10.1016/j.jpaa.2025.107969","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;em&gt;G&lt;/em&gt; be a finite group and &lt;span&gt;&lt;math&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;Irr&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Define &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;cv&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;Irr&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;cv&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and denote by &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;dl&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; the derived length of &lt;em&gt;G&lt;/em&gt;. In the 1990s Berkovich, Chillag and Zhmud described groups &lt;em&gt;G&lt;/em&gt; in which &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;cv&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; for every non-linear &lt;span&gt;&lt;math&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;Irr&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and their results show that &lt;em&gt;G&lt;/em&gt; is solvable. They also considered groups in which &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;cv&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; for some non-linear &lt;span&gt;&lt;math&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;Irr&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Continuing with their work, in this article, we prove that if &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;cv&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;⩽&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; for every non-linear &lt;span&gt;&lt;math&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;Irr&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, then &lt;em&gt;G&lt;/em&gt; is solvable. We also considered groups &lt;em&gt;G&lt;/em&gt; such that &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;cv&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;cd&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. T. Sakurai classified these groups in the case when &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;cd&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. We show that &lt;em&gt;G&lt;/em&gt; is solvable and we classify groups &lt;em&gt;G&lt;/em&gt; when &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;cd&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;⩽&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; or &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;dl&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⩽&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. It is interesting to note that these groups are such that &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;cv&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;⩽&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; for all &lt;span&gt;&lt;math&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;Irr&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Lastly, we consider finite groups &lt;em&gt;G&lt;/em&gt; with &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;cv&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;cd&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. For nilpotent groups","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107969"},"PeriodicalIF":0.7,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computation of the classifying ring of formal modules","authors":"A. Salch","doi":"10.1016/j.jpaa.2025.107975","DOIUrl":"10.1016/j.jpaa.2025.107975","url":null,"abstract":"<div><div>In this paper, we develop general machinery for computing the classifying ring <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>A</mi></mrow></msup></math></span> of one-dimensional formal <em>A</em>-modules, for various commutative rings <em>A</em>. We then apply the machinery to obtain calculations of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>A</mi></mrow></msup></math></span> for various number rings and cyclic group rings <em>A</em>. This includes the first full calculations of the ring <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>A</mi></mrow></msup></math></span> in cases in which it fails to be a polynomial algebra. We also derive consequences for the solvability of some lifting and extension problems.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107975"},"PeriodicalIF":0.7,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Groups with BCℓ-commutator relations","authors":"Egor Voronetsky","doi":"10.1016/j.jpaa.2025.107966","DOIUrl":"10.1016/j.jpaa.2025.107966","url":null,"abstract":"<div><div>Isotropic odd unitary groups generalize Chevalley groups of classical types over commutative rings and their twisted forms. Such groups have root subgroups parameterized by a root system <span><math><msub><mrow><mi>BC</mi></mrow><mrow><mi>ℓ</mi></mrow></msub></math></span> and may be constructed by so-called odd form rings with Peirce decompositions. We show the converse: if a group <em>G</em> has root subgroups indexed by roots of <span><math><msub><mrow><mi>BC</mi></mrow><mrow><mi>ℓ</mi></mrow></msub></math></span> and satisfying natural conditions, then there is a homomorphism <figure><img></figure> inducing isomorphisms on the root subgroups, where <figure><img></figure> is the odd unitary Steinberg group constructed by an odd form ring <span><math><mo>(</mo><mi>R</mi><mo>,</mo><mi>Δ</mi><mo>)</mo></math></span> with a Peirce decomposition. For groups with root subgroups indexed by <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>ℓ</mi></mrow></msub></math></span> (the already known case) the resulting odd form ring is essentially a generalized matrix ring.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 7","pages":"Article 107966"},"PeriodicalIF":0.7,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hilbert scheme of a pair of skew lines on cubic threefolds","authors":"Yilong Zhang","doi":"10.1016/j.jpaa.2025.107971","DOIUrl":"10.1016/j.jpaa.2025.107971","url":null,"abstract":"<div><div>Two general lines on a smooth cubic threefold <em>X</em> are disjoint and determine an irreducible component of the Hilbert scheme of <em>X</em>. We prove that this component is smooth and isomorphic to the Hilbert scheme of two points of the Fano varieties of lines of <em>X</em>. We also study its relation to the geometry of lines and singularities on the hyperplane sections of <em>X</em> and its relation to Bridgeland moduli spaces.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 6","pages":"Article 107971"},"PeriodicalIF":0.7,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143854737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}