关于Lie-Rinehart超代数的分类和变形

Q3 Mathematics
Quentin Ehret, A. Makhlouf
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引用次数: 0

摘要

本文的目的是研究Lie-Rinehart超代数的超特征零域,它由一个以某种方式相容的超交换结合超代数$a$和一个李超代数$L$组成。我们讨论了它们的结构,并提供了一个小维度的分类。我们描述了为$\dim(a)\leq2$和$\dim(L)\leq 4$定义Lie-Rinehart超代数的所有可能对。此外,我们构造了一个上同调复形,并在形式幂级数和上同调的基础上发展了形式变形理论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On classification and deformations of Lie-Rinehart superalgebras
The purpose of this paper is to study Lie-Rinehart superalgebras over characteristic zero fields, which are consisting of a supercommutative associative superalgebra $A$ and a Lie superalgebra $L$ that are compatible in a certain way. We discuss their structure and provide a classification in small dimensions. We describe all possible pairs defining a Lie-Rinehart superalgebra for $\dim(A)\leq 2$ and $\dim(L)\leq 4$. Moreover, we construct a cohomology complex and develop a theory of formal deformations based on formal power series and this cohomology.
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来源期刊
Communications in Mathematics
Communications in Mathematics Mathematics-Mathematics (all)
CiteScore
1.00
自引率
0.00%
发文量
26
审稿时长
45 weeks
期刊介绍: Communications in Mathematics publishes research and survey papers in all areas of pure and applied mathematics. To be acceptable for publication, the paper must be significant, original and correct. High quality review papers of interest to a wide range of scientists in mathematics and its applications are equally welcome.
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