Journal of Pure and Applied Algebra最新文献

{"title":"On irreducibility of modules of Whittaker type: Twisted modules and nonabelian orbifolds","authors":"Dražen Adamović ,&nbsp;Ching Hung Lam ,&nbsp;Veronika Pedić Tomić ,&nbsp;Nina Yu","doi":"10.1016/j.jpaa.2024.107840","DOIUrl":"10.1016/j.jpaa.2024.107840","url":null,"abstract":"<div><div>In <span><span>[1]</span></span>, we extended the Dong-Mason theorem on irreducibility of modules for cyclic orbifold vertex algebras (cf. <span><span>[12]</span></span>) to the entire category of weak modules and applied this result to Whittaker modules. In this paper, we present further generalizations of these results for nonabelian orbifolds of vertex operator superalgebras. Let <em>V</em> be a vertex superalgebra of a countable dimension and let <em>G</em> be a finite subgroup of <span><math><mrow><mi>Aut</mi></mrow><mo>(</mo><mi>V</mi><mo>)</mo></math></span>. Assume that <span><math><mi>h</mi><mo>∈</mo><mi>Z</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> where <span><math><mi>Z</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is the center of the group <em>G</em>. For any irreducible <em>h</em>–twisted (weak) <em>V</em>–module <em>M</em>, we prove that if <span><math><mi>M</mi><mo>≇</mo><mi>g</mi><mo>∘</mo><mi>M</mi></math></span> for all <span><math><mi>g</mi><mo>∈</mo><mi>G</mi></math></span> then <em>M</em> is also irreducible as <span><math><msup><mrow><mi>V</mi></mrow><mrow><mi>G</mi></mrow></msup></math></span>–module. We also apply this result to examples and give irreducibility of modules of Whittaker type for orbifolds of Neveu-Schwarz vertex superalgebras, Heisenberg vertex algebras, Virasoro vertex operator algebra and Heisenberg-Virasoro vertex algebra.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107840"},"PeriodicalIF":0.7,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723156","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 cohomology of Lie algebras associated with graphs","authors":"Marco Aldi ,&nbsp;Andrew Butler ,&nbsp;Jordan Gardiner ,&nbsp;Daniele Grandini ,&nbsp;Monica Lichtenwalner ,&nbsp;Kevin Pan","doi":"10.1016/j.jpaa.2024.107838","DOIUrl":"10.1016/j.jpaa.2024.107838","url":null,"abstract":"<div><div>We describe a canonical decomposition of the cohomology of the Dani-Mainkar 2-step nilpotent Lie algebras associated with graphs. As applications, we obtain explicit formulas for the third cohomology of any Dani-Mainkar Lie algebra and for the cohomology in all degrees of Lie algebras associated with arbitrary star graphs. We also describe a procedure to reduce the calculation of the cohomology of solvable Lie algebras associated with graphs through the Grantcharov-Grantcharov-Iliev construction to the cohomology of Dani-Mainkar Lie algebras.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107838"},"PeriodicalIF":0.7,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705835","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":"Normalizer quotients of symmetric groups and inner holomorphs","authors":"Alexei Entin ,&nbsp;Cindy (Sin Yi) Tsang","doi":"10.1016/j.jpaa.2024.107839","DOIUrl":"10.1016/j.jpaa.2024.107839","url":null,"abstract":"<div><div>We show that every finite group <em>T</em> is isomorphic to a normalizer quotient <span><math><msub><mrow><mi>N</mi></mrow><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub><mo>(</mo><mi>H</mi><mo>)</mo><mo>/</mo><mi>H</mi></math></span> for some <em>n</em> and a subgroup <span><math><mi>H</mi><mo>≤</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. We show that this holds for all large enough <span><math><mi>n</mi><mo>≥</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>T</mi><mo>)</mo></math></span> and also with <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> replaced by <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. The two main ingredients in the proof are a recent construction due to Cornulier and Sambale of a finite group <em>G</em> with <span><math><mrow><mi>Out</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>≅</mo><mi>T</mi></math></span> (for any given finite group <em>T</em>) and the determination of the normalizer in <span><math><mrow><mi>Sym</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of the inner holomorph <span><math><mrow><mi>InHol</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mrow><mi>Sym</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math></span> for any centerless indecomposable finite group <em>G</em>, which may be of independent interest.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107839"},"PeriodicalIF":0.7,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705833","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":"Laumon parahoric local models via quiver Grassmannians","authors":"Evgeny Feigin ,&nbsp;Martina Lanini ,&nbsp;Alexander Pütz","doi":"10.1016/j.jpaa.2024.107837","DOIUrl":"10.1016/j.jpaa.2024.107837","url":null,"abstract":"<div><div>Local models of Shimura varieties in type A can be realized inside products of Grassmannians via certain linear algebraic conditions. Laumon suggested a generalization which can be identified with a family over a line whose general fibers are quiver Grassmannians for the loop quiver and the special fiber is a certain quiver Grassmannian for the cyclic quiver. The whole family sits inside the Gaitsgory central degeneration of the affine Grassmannians. We study the properties of the special fibers of the (complex) Laumon local models for arbitrary parahoric subgroups in type A using the machinery of quiver representations. We describe the irreducible components and the natural strata with respect to the group action for the quiver Grassmannians in question. We also construct a cellular decomposition and provide an explicit description for the corresponding poset of cells. Finally, we study the properties of the desingularizations of the irreducible components and show that the desingularization construction is compatible with the natural projections between the parahoric subgroups.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107837"},"PeriodicalIF":0.7,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Period integrals of smooth projective complete intersections as exponential periods","authors":"Jeehoon Park","doi":"10.1016/j.jpaa.2024.107836","DOIUrl":"10.1016/j.jpaa.2024.107836","url":null,"abstract":"<div><div>Let <em>X</em> be a smooth projective complete intersection over <span><math><mi>Q</mi></math></span> of dimension <span><math><mi>n</mi><mo>−</mo><mi>k</mi></math></span> in the projective space <span><math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> defined by the zero locus of <span><math><munder><mrow><mi>f</mi></mrow><mo>_</mo></munder><mo>(</mo><munder><mrow><mi>x</mi></mrow><mo>_</mo></munder><mo>)</mo><mo>=</mo><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><munder><mrow><mi>x</mi></mrow><mo>_</mo></munder><mo>)</mo><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><munder><mrow><mi>x</mi></mrow><mo>_</mo></munder><mo>)</mo><mo>)</mo></math></span>, for given positive integers <em>n</em> and <em>k</em>. For a given primitive homology cycle <span><math><mo>[</mo><mi>γ</mi><mo>]</mo><mo>∈</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow></msub><msub><mrow><mo>(</mo><mi>X</mi><mo>(</mo><mi>C</mi><mo>)</mo><mo>,</mo><mi>Z</mi><mo>)</mo></mrow><mrow><mn>0</mn></mrow></msub></math></span>, the period integral is defined to be a linear map from the primitive de Rham cohomology group <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mi>d</mi><mi>R</mi><mo>,</mo><mi>prim</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow></msubsup><mo>(</mo><mi>X</mi><mo>(</mo><mi>C</mi><mo>)</mo><mo>;</mo><mi>Q</mi><mo>)</mo></math></span> to <span><math><mi>C</mi></math></span> given by <span><math><mo>[</mo><mi>ω</mi><mo>]</mo><mo>↦</mo><msub><mrow><mo>∫</mo></mrow><mrow><mi>γ</mi></mrow></msub><mi>ω</mi></math></span>. The goal of this article is to interpret this period integral as <em>Feynman's path integral</em> of 0-dimensional quantum field theory with the action functional <span><math><mi>S</mi><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>ℓ</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>k</mi></mrow></msubsup><msub><mrow><mi>y</mi></mrow><mrow><mi>ℓ</mi></mrow></msub><msub><mrow><mi>f</mi></mrow><mrow><mi>ℓ</mi></mrow></msub><mo>(</mo><munder><mrow><mi>x</mi></mrow><mo>_</mo></munder><mo>)</mo></math></span> (in other words, <em>the exponential period</em> with the action functional <em>S</em>) and use this interpretation to develop a formal deformation theory of period integrals of <em>X</em>, which can be viewed as a modern deformation theoretic treatment of the period integrals based on the Maurer-Cartan equation of a dgla (differential graded Lie algebra).</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107836"},"PeriodicalIF":0.7,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654093","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":"GT-shadows for the gentle version GTˆgen of the Grothendieck-Teichmueller group","authors":"Vasily A. Dolgushev ,&nbsp;Jacob J. Guynee","doi":"10.1016/j.jpaa.2024.107819","DOIUrl":"10.1016/j.jpaa.2024.107819","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>B</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> be the Artin braid group on 3 strands and <span><math><msub><mrow><mi>PB</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> be the corresponding pure braid group. In this paper, we construct the groupoid <span><math><mi>GTSh</mi></math></span> of <span><math><mi>GT</mi></math></span>-shadows for a (possibly more tractable) version <span><math><msub><mrow><mover><mrow><mi>GT</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msub></math></span> of the Grothendieck-Teichmueller group <span><math><mover><mrow><mi>GT</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> introduced in paper <span><span>[12]</span></span> by D. Harbater and L. Schneps. We call this group the gentle version of <span><math><mover><mrow><mi>GT</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> and denote it by <span><math><msub><mrow><mover><mrow><mi>GT</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mi>g</mi><mi>e</mi><mi>n</mi></mrow></msub></math></span>. The objects of <span><math><mi>GTSh</mi></math></span> are finite index normal subgroups <span><math><mi>N</mi></math></span> of <span><math><msub><mrow><mi>B</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> satisfying the condition <span><math><mi>N</mi><mo>≤</mo><msub><mrow><mi>PB</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>. Morphisms of <span><math><mi>GTSh</mi></math></span> are called <span><math><mi>GT</mi></math></span>-shadows and they may be thought of as approximations to elements of <span><math><msub><mrow><mover><mrow><mi>GT</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mi>g</mi><mi>e</mi><mi>n</mi></mrow></msub></math></span>. We show how <span><math><mi>GT</mi></math></span>-shadows can be obtained from elements of <span><math><msub><mrow><mover><mrow><mi>GT</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mi>g</mi><mi>e</mi><mi>n</mi></mrow></msub></math></span> and prove that <span><math><msub><mrow><mover><mrow><mi>GT</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mi>g</mi><mi>e</mi><mi>n</mi></mrow></msub></math></span> is isomorphic to the limit of a certain functor defined in terms of the groupoid <span><math><mi>GTSh</mi></math></span>. Using this result, we get a criterion for identifying genuine <span><math><mi>GT</mi></math></span>-shadows.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107819"},"PeriodicalIF":0.7,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705834","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 Gowers trick for classical simple groups","authors":"Francesco Fumagalli ,&nbsp;Attila Maróti","doi":"10.1016/j.jpaa.2024.107833","DOIUrl":"10.1016/j.jpaa.2024.107833","url":null,"abstract":"<div><div>If <em>A</em>, <em>B</em>, <em>C</em> are subsets in a finite simple group of Lie type <em>G</em> at least two of which are normal with <span><math><mo>|</mo><mi>A</mi><mo>|</mo><mo>|</mo><mi>B</mi><mo>|</mo><mo>|</mo><mi>C</mi><mo>|</mo></math></span> relatively large, then we establish a stronger conclusion than <span><math><mi>A</mi><mi>B</mi><mi>C</mi><mo>=</mo><mi>G</mi></math></span>. This is related to a theorem of Gowers and is a generalization of a theorem of Larsen, Shalev, Tiep and the second author and Pyber.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107833"},"PeriodicalIF":0.7,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flat relative Mittag-Leffler modules and Zariski locality","authors":"Asmae Ben Yassine,&nbsp;Jan Trlifaj","doi":"10.1016/j.jpaa.2024.107834","DOIUrl":"10.1016/j.jpaa.2024.107834","url":null,"abstract":"<div><div>The ascent and descent of the Mittag-Leffler property were instrumental in proving Zariski locality of the notion of an (infinite dimensional) vector bundle by Raynaud and Gruson in <span><span>[26]</span></span>. More recently, relative Mittag-Leffler modules were employed in the theory of (infinitely generated) tilting modules and the associated quasi-coherent sheaves, <span><span>[2]</span></span>, <span><span>[22]</span></span>. Here, we study the ascent and descent along flat and faithfully flat homomorphisms for relative versions of the Mittag-Leffler property. In particular, we prove the Zariski locality of the notion of a locally f-projective quasi-coherent sheaf for all schemes, and for each <span><math><mi>n</mi><mo>≥</mo><mn>1</mn></math></span>, of the notion of an <em>n</em>-Drinfeld vector bundle for all locally noetherian schemes.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107834"},"PeriodicalIF":0.7,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552393","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":"Almost Gorenstein simplicial semigroup rings","authors":"Kazufumi Eto ,&nbsp;Naoyuki Matsuoka ,&nbsp;Takahiro Numata ,&nbsp;Kei-ichi Watanabe","doi":"10.1016/j.jpaa.2024.107835","DOIUrl":"10.1016/j.jpaa.2024.107835","url":null,"abstract":"<div><div>We give a criterion for almost Gorenstein property for semigroup rings associated with simplicial semigroups. We extend Nari's theorem for almost symmetric numerical semigroups to simplicial semigroups with higher rank. By this criterion, we determine 2-dimensional normal semigroup rings which have “Ulrich elements” defined in <span><span>[8]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107835"},"PeriodicalIF":0.7,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"DK conjecture for some K-inequivalences from Grassmannians","authors":"Naichung Conan Leung ,&nbsp;Ying Xie","doi":"10.1016/j.jpaa.2024.107831","DOIUrl":"10.1016/j.jpaa.2024.107831","url":null,"abstract":"<div><div>The DK conjecture of Bondal-Orlov <span><span>[1]</span></span> and Kawamata <span><span>[2]</span></span> states that there should be an embedding of bounded derived categories for any <em>K</em>-inequivalence, which is proved to be true for the toroidal case (<span><span>[3]</span></span>, <span><span>[4]</span></span>, <span><span>[5]</span></span> and <span><span>[6]</span></span>). In this paper, we construct examples of non-toroidal <em>K</em>-inequivalences from Grassmannians inspired by <span><span>[7]</span></span>, <span><span>[8]</span></span>, <span><span>[9]</span></span> and <span><span>[10]</span></span>, and we show that these <em>K</em>-inequivalences satisfy the DK conjecture.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107831"},"PeriodicalIF":0.7,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654092","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}