Journal of Pure and Applied Algebra最新文献

{"title":"Graph complexes and deformation theories of the (wheeled) properads of quasi- and pseudo-Lie bialgebras","authors":"Oskar Frost","doi":"10.1016/j.jpaa.2026.108204","DOIUrl":"10.1016/j.jpaa.2026.108204","url":null,"abstract":"<div><div>Quasi-Lie bialgebras are natural extensions of Lie bialgebras, where the cobracket satisfies the co-Jacobi relation up to some natural obstruction controlled by a skew-symmetric 3-tensor <em>ϕ</em>. This structure was introduced by Drinfeld while studying deformation theory of universal enveloping algebras and has since seen many other applications in algebra and geometry. In this paper we study the derivation complex of strongly homotopy quasi-Lie bialgebra, both in the unwheeled (i.e. standard) and wheeled case, and compute its cohomology in terms of Kontsevich graph complexes.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108204"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147422584","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":"Infinite dimensional modules for linear algebraic groups","authors":"Eric M. Friedlander","doi":"10.1016/j.jpaa.2026.108206","DOIUrl":"10.1016/j.jpaa.2026.108206","url":null,"abstract":"<div><div>We investigate infinite dimensional modules for a linear algebraic group <span><math><mi>G</mi></math></span> over a field of positive characteristic <em>p</em>. For any subcoalgebra <span><math><mi>C</mi><mo>⊂</mo><mi>O</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of the coordinate algebra of <span><math><mi>G</mi></math></span>, we consider the abelian subcategory <span><math><mi>C</mi><mi>o</mi><mi>M</mi><mi>o</mi><mi>d</mi><mo>(</mo><mi>C</mi><mo>)</mo><mo>⊂</mo><mi>M</mi><mi>o</mi><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and the left exact functor <span><math><msub><mrow><mo>(</mo><mo>−</mo><mo>)</mo></mrow><mrow><mi>C</mi></mrow></msub><mo>:</mo><mi>M</mi><mi>o</mi><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>→</mo><mi>C</mi><mi>o</mi><mi>M</mi><mi>o</mi><mi>d</mi><mo>(</mo><mi>C</mi><mo>)</mo></math></span> that is right adjoint to the inclusion functor. The class of cofinite <span><math><mi>G</mi></math></span>-modules is formulated using finite dimensional subcoalgebras of <span><math><mi>O</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and the polynomial growth of various examples of cofinite modules is computed.</div><div>Infinite dimensional <span><math><mi>G</mi></math></span>-modules of particular interest are those which are mock injective. Various examples of mock injective modules are investigated. For almost all linear algebraic groups <span><math><mi>G</mi></math></span>, every mock injective <span><math><mi>G</mi></math></span>-module <em>J</em> satisfies the condition that <span><math><mi>H</mi><mi>o</mi><msub><mrow><mi>m</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>J</mi><mo>,</mo><mi>M</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span> whenever <span><math><mi>M</mi><mo>=</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>C</mi></mrow></msub></math></span> for some finite dimensional sub-coalgebra <span><math><mi>C</mi><mo>⊂</mo><mi>O</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108206"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147422583","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":"On the strong Sarkisov program","authors":"Yang He","doi":"10.1016/j.jpaa.2026.108208","DOIUrl":"10.1016/j.jpaa.2026.108208","url":null,"abstract":"<div><div>In this paper, we showed that the strong Sarkisov program in dimension <em>d</em> can be derived from the termination of specific log flips in dimension <span><math><mo>≤</mo><mi>d</mi><mo>−</mo><mn>1</mn></math></span>. As a corollary, we prove that the strong Sarkisov program holds in dimension 4. Additionally, we prove the weak Sarkisov program with decreasing (augmented) Sarkisov degree. Finally, using the theory of syzygies of Mori fibre spaces, we obtain a directed diagram that encodes the information of the strong Sarkisov program.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108208"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147422553","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":"Bilinear secants and birational geometry of blowups of Pn×Pn+1","authors":"Elisa Postinghel ,&nbsp;Artie Prendergast-Smith","doi":"10.1016/j.jpaa.2026.108194","DOIUrl":"10.1016/j.jpaa.2026.108194","url":null,"abstract":"<div><div>We introduce bilinear secant varieties and joins of subvarieties of products of projective spaces, as a generalisation of the classical secant varieties and joins of projective varieties. We show that the bilinear secant varieties of certain rational normal curves of <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> play a central role in the study of the birational geometry of <span><math><msubsup><mrow><mi>X</mi></mrow><mrow><mi>s</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup></math></span>, its blow-up in <em>s</em> points in general position. We show that <span><math><msubsup><mrow><mi>X</mi></mrow><mrow><mi>s</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup></math></span> is log Fano, and we compute its effective and movable cones, for <span><math><mi>s</mi><mo>≤</mo><mi>n</mi><mo>+</mo><mn>2</mn></math></span> and <span><math><mi>n</mi><mo>≥</mo><mn>1</mn></math></span> and for <span><math><mi>s</mi><mo>≤</mo><mi>n</mi><mo>+</mo><mn>3</mn></math></span> and <span><math><mi>n</mi><mo>≤</mo><mn>2</mn></math></span>, and we compute the effective and movable cones of <span><math><msubsup><mrow><mi>X</mi></mrow><mrow><mn>6</mn></mrow><mrow><mn>3</mn><mo>,</mo><mn>4</mn></mrow></msubsup></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108194"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147422566","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":"Demazure operators for double cosets","authors":"Ben Elias ,&nbsp;Hankyung Ko ,&nbsp;Nicolas Libedinsky ,&nbsp;Leonardo Patimo","doi":"10.1016/j.jpaa.2026.108207","DOIUrl":"10.1016/j.jpaa.2026.108207","url":null,"abstract":"<div><div>For any Coxeter system, and any double coset for two standard parabolic subgroups, we introduce a Demazure operator. These operators form a basis for morphism spaces in a category we call the nilCoxeter category, and we also present this category by generators and relations. We prove a generalization to this context of Demazure's celebrated theorem on Frobenius extensions. This generalized theorem serves as a criterion for ensuring the proper behavior of singular Soergel bimodules.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108207"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147422586","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":"A polyhedral approach to the invariant of Bierstone and Milman","authors":"Bernd Schober","doi":"10.1016/j.jpaa.2026.108191","DOIUrl":"10.1016/j.jpaa.2026.108191","url":null,"abstract":"<div><div>Based on previous work by the author we deduce that the invariant introduced by Bierstone and Milman in order to give a proof for constructive resolution of singularities in characteristic zero can be determined purely by considering certain polyhedra and their projections.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108191"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147422567","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":"On the Σ1 and Σ2-invariants of Artin groups","authors":"Marcos Escartín-Ferrer","doi":"10.1016/j.jpaa.2026.108209","DOIUrl":"10.1016/j.jpaa.2026.108209","url":null,"abstract":"<div><div>We prove the <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-conjecture for two families of Artin groups: Artin groups such that there exists a prime number <em>p</em> dividing <span><math><mfrac><mrow><mi>l</mi><mo>(</mo><mi>e</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> for every edge <em>e</em> with even label &gt;2 and balanced Artin groups. The family of balanced Artin groups extends two previously studied families: the one considered by Kochloukova in <span><span>[19]</span></span> and the family of coherent Artin groups. We state a conjecture on the <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-invariant for Artin groups satisfying the <span><math><mi>K</mi><mo>(</mo><mi>π</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-conjecture. The conjecture is proven to be true for two significant families: 2-dimensional and coherent Artin groups. In the 2-dimensional case we are able to compute <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> for all <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span> and to derive finiteness properties of the derived subgroup.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108209"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147422570","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":"Monoidal relative categories model monoidal ∞-categories","authors":"Kensuke Arakawa","doi":"10.1016/j.jpaa.2026.108183","DOIUrl":"10.1016/j.jpaa.2026.108183","url":null,"abstract":"<div><div>We prove that the homotopy theory of monoidal relative categories is equivalent to that of monoidal ∞-categories, and likewise in the symmetric monoidal setting. As an application, we give a concise and complete proof of the fact that every presentably monoidal or presentably symmetric monoidal ∞-category is presented by a monoidal or symmetric monoidal model category, which, in the monoidal case, was sketched by Lurie, and in the symmetric monoidal case, was proved by Nikolaus–Sagave.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108183"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079527","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":"Betti cones over fibre products","authors":"H. Ananthnarayan ,&nbsp;Omkar Javadekar ,&nbsp;Rajiv Kumar","doi":"10.1016/j.jpaa.2026.108181","DOIUrl":"10.1016/j.jpaa.2026.108181","url":null,"abstract":"<div><div>Let <em>R</em> be a fibre product of standard graded algebras over a field. We study the structure of syzygies of finitely generated graded <em>R</em>-modules and the Koszul property of <em>R</em>. As an application of this, we show that the existence of an <em>R</em>-module of finite regularity and infinite projective dimension forces <em>R</em> to be Koszul. We also look at the extremal rays of the Betti cone of finitely generated graded <em>R</em>-modules, and show that when <span><math><mtext>depth</mtext><mo>(</mo><mi>R</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></span>, they are spanned by the Betti tables of pure <em>R</em>-modules if and only if <em>R</em> is Cohen–Macaulay with minimal multiplicity.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108181"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079528","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":"Images of polynomial maps and the Ax-Grothendieck theorem over algebraically closed division rings","authors":"Elad Paran ,&nbsp;Tran Nam Son","doi":"10.1016/j.jpaa.2026.108186","DOIUrl":"10.1016/j.jpaa.2026.108186","url":null,"abstract":"<div><div>We study the images of polynomial maps over algebraically closed division rings. Our first result generalizes the classical Ax-Grothendieck theorem: We show that if <span><math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> are elements of the free associative algebra <span><math><mi>D</mi><mo>〈</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>〉</mo></math></span> generated by <span><math><mi>m</mi><mo>≥</mo><mn>1</mn></math></span> variables over an algebraically closed division ring <em>D</em> of finite dimension over its center <em>F</em>, and if the induced map <span><math><mi>f</mi><mo>=</mo><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo><mo>:</mo><msup><mrow><mi>D</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>→</mo><msup><mrow><mi>D</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> is injective, then <em>f</em> must be surjective. With no condition on the dimension over the center, our second result is that <span><math><mi>p</mi><mo>(</mo><mi>D</mi><mo>)</mo><mo>=</mo><mi>D</mi></math></span> if <em>p</em> is either an element in <span><math><mi>F</mi><mo>〈</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>〉</mo></math></span> with zero constant term such that <span><math><mi>p</mi><mo>(</mo><mi>F</mi><mo>)</mo><mo>≠</mo><mo>{</mo><mn>0</mn><mo>}</mo></math></span>, or a nonconstant polynomial in <span><math><mi>F</mi><mo>[</mo><mi>x</mi><mo>]</mo></math></span>. Furthermore, we also establish some Waring type results. For instance, for any integer <span><math><mi>n</mi><mo>&gt;</mo><mn>1</mn></math></span>, we prove that every matrix in <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>D</mi><mo>)</mo></math></span> can be expressed as a difference of pairs of multiplicative commutators of elements from <span><math><mi>p</mi><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>D</mi><mo>)</mo><mo>)</mo></math></span>, provided again that <em>D</em> is finite-dimensional over <em>F</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108186"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079526","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}