The homology of the Brauer algebras

Rachael  Boyd; Richard Hepworth; Peter Patzt

doi:10.1007/s00029-021-00697-4

The homology of the Brauer algebras

Rachael Boyd, Richard Hepworth, Peter Patzt

Institut for Matematiske Fag

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

10 Citationer (Scopus)

28 Downloads (Pure)

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 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 the parameter is not invertible, this isomorphism still holds in a range of degrees that increases with n.

Originalsprog	Engelsk
Artikelnummer	85
Tidsskrift	Selecta Mathematica
Vol/bind	27
Sider (fra-til)	1-31
ISSN	1022-1824
DOI	https://doi.org/10.1007/s00029-021-00697-4
Status	Udgivet - 2021

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10.1007/s00029-021-00697-4Licens: CC BY

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Citationsformater

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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 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 the parameter is not invertible, this isomorphism still holds in a range of degrees that increases with n. ",

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AB - 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 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 the parameter is not invertible, this isomorphism still holds in a range of degrees that increases with n.

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