Journal of Pure and Applied Algebra最新文献_第6页

The second homology group of the commutative case of Kontsevich's symplectic derivation Lie algebra

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107841

Shuichi Harako

{"title":"The second homology group of the commutative case of Kontsevich's symplectic derivation Lie algebra","authors":"Shuichi Harako","doi":"10.1016/j.jpaa.2024.107841","DOIUrl":"10.1016/j.jpaa.2024.107841","url":null,"abstract":"<div><div>In 1993, Kontsevich introduced the symplectic derivation Lie algebras related to various geometric objects including moduli spaces of graphs and of Riemann surfaces, graph homologies, Hamiltonian vector fields, etc. Each of them is a graded algebra, so that its Chevalley-Eilenberg chain complex has another <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mo>≥</mo><mn>0</mn></mrow></msub></math></span>-grading, called weight, than the usual homological degree. We focus on one of the Lie algebras <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span>, called the “commutative case”, and its positive weight part <span><math><msubsup><mrow><mi>c</mi></mrow><mrow><mi>g</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>⊂</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span>. The symplectic invariant homology of <span><math><msubsup><mrow><mi>c</mi></mrow><mrow><mi>g</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math></span> is closely related to the commutative graph homology, hence some computational results are obtained from the viewpoint of graph homology theory. On the other hand, the details of the entire homology group <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>•</mo></mrow></msub><mo>(</mo><msubsup><mrow><mi>c</mi></mrow><mrow><mi>g</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>)</mo></math></span> are not completely known. We determine <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><msubsup><mrow><mi>c</mi></mrow><mrow><mi>g</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>)</mo></math></span> by decomposing it by weight and using the classical representation theory of the symplectic groups.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107841"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143094012","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}

引用次数: 0

Group-graded twisted Calabi–Yau algebras

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107849

Yasmeen S. Baki

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Kernels of linear maps

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107847

Arno van den Essen , Jan Schoone

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Topology and monoid representations I: Foundations

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107848

Benjamin Steinberg

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Rings of almost everywhere defined functions

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107851

Matthias Schötz

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Fano manifolds whose Chern characters satisfy some positivity conditions

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2025.107865

Taku Suzuki

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Retraction notice to “On the fifth Singer algebraic transfer in a generic family of internal degree characterized by μ(n)=4” [J. Pure Appl. Algebra 228 (2024) 107658]

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2025.107873

Đặng Võ Phúc

{"title":"Retraction notice to “On the fifth Singer algebraic transfer in a generic family of internal degree characterized by μ(n)=4” [J. Pure Appl. Algebra 228 (2024) 107658]","authors":"Đặng Võ Phúc","doi":"10.1016/j.jpaa.2025.107873","DOIUrl":"10.1016/j.jpaa.2025.107873","url":null,"abstract":"<div><div>This article has been retracted: please see Elsevier Policy on Article Withdrawal (<span><span>https://www.elsevier.com/about/policies/article-withdrawal</span><svg><path></path></svg></span>).</div><div>This article has been retracted at the request of the Editors-in-Chief.</div><div>Many of the results in this paper are false, including the main result (Theorem 1.3), whose proof has a mistake, and several of its consequences are asserted without proof. In a letter to the Editors providing comments to the paper, a colleague pointed out that a proof is only provided for the cases <span><math><mo>(</mo><mi>k</mi><mo>,</mo><mi>s</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>8</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> and <span><math><mo>(</mo><mn>10</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, asserting that the main result is false for <span><math><mo>(</mo><mi>k</mi><mo>,</mo><mi>s</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>8</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> and also incomplete for <span><math><mo>(</mo><mn>10</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>. No proof is given for <span><math><mi>s</mi><mo>></mo><mn>2</mn></math></span>.</div><div>A detailed assessment by independent referees created reasonable doubt that the author's results were correct.</div><div>The Corrigendum to this article does not provide any proofs, but points out an “inaccuracy” in a different part of the paper (Cor. 1.11).</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107873"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143099043","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}

引用次数: 0

Directed graphs, Frattini-resistance, and maximal pro-p Galois groups

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107857

Claudio Quadrelli

引用次数: 0

The multiple holomorph of centerless groups

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107843

Cindy (Sin Yi) Tsang

{"title":"The multiple holomorph of centerless groups","authors":"Cindy (Sin Yi) Tsang","doi":"10.1016/j.jpaa.2024.107843","DOIUrl":"10.1016/j.jpaa.2024.107843","url":null,"abstract":"<div><div>Let <em>G</em> be a group. The holomorph <span><math><mrow><mi>Hol</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of <em>G</em> may be defined as the normalizer of the subgroup of either left or right translations in the group of all permutations of <em>G</em>. The multiple holomorph <span><math><mrow><mi>NHol</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is in turn defined as the normalizer of the holomorph. Their quotient <span><math><mi>T</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mrow><mi>NHol</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>/</mo><mrow><mi>Hol</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math></span> has been computed for various families of groups <em>G</em>. In this paper, we consider the case when <em>G</em> is centerless, and we show that <span><math><mi>T</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> must have exponent at most 2 unless <em>G</em> satisfies some fairly strong conditions. As applications of our main theorem, we are able to show that <span><math><mi>T</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> has order 2 for all almost simple groups <em>G</em>, and that <span><math><mi>T</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> has exponent at most 2 for all centerless perfect or complete groups <em>G</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107843"},"PeriodicalIF":0.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143094011","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}

引用次数: 0

Relative extensions and cohomology of profinite groups

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI: 10.1016/j.jpaa.2024.107846

Gareth Wilkes

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