论受限海森堡李代数的同调性

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-07-03 DOI:10.1016/j.laa.2024.06.027

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引用次数: 0

摘要

我们证明了特征域上的海森堡李代数包含一个受限李代数家族，并对所有这些非同构的受限李代数结构进行了分类。我们使用具有三系数的普通 1-和 2-同调空间来计算这些受限海森堡李代数的受限 1-和 2-同调空间。我们描述了受限一维中心扩展，包括列括号和-运算符的明确公式。

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On the cohomology of restricted Heisenberg Lie algebras

We show that the Heisenberg Lie algebras over a field $F$ of characteristic $p > 0$ admit a family of restricted Lie algebras, and we classify all such non-isomorphic restricted Lie algebra structures. We use the ordinary 1- and 2-cohomology spaces with trivial coefficients to compute the restricted 1- and 2-cohomology spaces of these restricted Heisenberg Lie algebras. We describe the restricted 1-dimensional central extensions, including explicit formulas for the Lie brackets and $\cdot^{[p]}$ -operators.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.