对称群的Hochschild上同调与生成函数

Pub Date : 2023-03-09 DOI:10.1515/jgth-2022-0130

D. Benson, R. Kessar, M. Linckelmann

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引用次数: 1

摘要

本文计算了低次素数域上对称群的Hochschild上同调的维数。这涉及到我们研究对称群的Hochschild上同调的任意固定次维的一些划分恒等式和生成函数。证明了对称群在任意定次上的Hochschild上同调维的生成函数与在0次上的生成函数有一个有理数的不同。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hochschild cohomology of symmetric groups and generating functions

Abstract In this article, we compute the dimensions of the Hochschild cohomology of symmetric groups over prime fields in low degrees. This involves us in studying some partition identities and generating functions of the dimensions in any fixed degree of the Hochschild cohomology of symmetric groups. We show that the generating function of the dimensions of the Hochschild cohomology in any fixed degree of the symmetric groups differs from that in degree 0 by a rational function.

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