Hochschild cohomology of symmetric groups and generating functions

Author:

Benson David1,Kessar Radha2,Linckelmann Markus3

Affiliation:

1. Institute of Mathematics , Fraser Noble Building , University of Aberdeen , King’s College , Aberdeen AB24 3UE , United Kingdom

2. Department of Mathematics , The University of Manchester , Oxford Road , Manchester M13 9PL , United Kingdom

3. School of Mathematics, Computer Science & Engineering , Department of Mathematics , City , University of London , Northampton Square , London EC1V 0HB , United Kingdom

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference11 articles.

1. G. E. Andrews and E. Deutsch, A note on a method of Erdős and the Stanley–Elder theorems, Integers 16 (2016), Paper No. A24.

2. D. J. Benson, Representations and Cohomology. II: Cohomology of Groups and Modules, 2nd ed., Cambridge Stud. Adv. Math. 31, Cambridge University, Cambridge, 1998.

3. B. Briggs and L. Rubio y Degrassi, On the Lie algebra structure of integrable derivations, preprint (2022), https://arxiv.org/abs/2205.01660.

4. N. J. Fine, Sums over partitions, Report of the Institute in the Theory of Numbers, University of Colorado, Boulder (1959), 86–84.

5. R. A. Gilbert, A Fine rediscovery, Amer. Math. Monthly 122 (2015), no. 4, 322–331.

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the Lie algebra structure of integrable derivations;Bulletin of the London Mathematical Society;2023-07-06

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