论与图相关的李代数同调

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2024-11-14 DOI:10.1016/j.jpaa.2024.107838

Marco Aldi , Andrew Butler , Jordan Gardiner , Daniele Grandini , Monica Lichtenwalner , Kevin Pan

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引用次数: 0

摘要

我们描述了与图相关的丹尼-马恩卡 2 阶零能烈代数的同调的规范分解。作为应用，我们得到了任何 Dani-Mainkar Lie 代数的第三同调的明确公式，以及与任意星形图相关的 Lie 代数的所有度数的同调的明确公式。我们还描述了通过格兰查洛夫-格兰查洛夫-伊利耶夫构造将与图相关的可解李代数的同调计算简化为丹尼-马恩卡尔李代数的同调计算的过程。

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On the cohomology of Lie algebras associated with graphs

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.

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来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.