The homology of the Brauer algebras

Rachel  Boyd; Richard Hepworth; Peter  Patzt

doi:10.1007/s00029-021-00697-4

The homology of the Brauer algebras

Rachel Boyd, Richard Hepworth, Peter Patzt

Mathematical Science

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4 Citations (Scopus)

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Abstract

This paper investigates the homology of the Brauer algebras, interpreted as appropriate Tor-groups, and shows that it is closely related to the homology of the symmetric group. Our main results show that when the defining parameter δ of the Brauer algebra is invertible, then the homology of the Brauer algebra is isomorphic to the homology of the symmetric group, and that when δ is not invertible, this isomorphism still holds in a range of degrees that increases with n.

Original language	English
Article number	85
Number of pages	31
Journal	Selecta Mathematica
Volume	27
Issue number	5
Early online date	25 Aug 2021
DOIs	https://doi.org/10.1007/s00029-021-00697-4
Publication status	Published - 2021

Bibliographical note

Peter Patzt was supported by the Danish National Research Foundation through the Copenhagen Centre for Geometry and Topology (DNRF151) and the European Research Council under the European Union’s Seventh Framework Programme ERC Grant agreement ERC StG 716424 - CASe, PI Karim Adiprasito

Keywords

Homology
Homological stability
Brauer algebras

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Cite this

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KW - Homological stability

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JF - Selecta Mathematica

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The homology of the Brauer algebras

Abstract

Bibliographical note

Keywords

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