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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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

Keywords

Homology
Homological stability
Brauer algebras

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Cite this

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PY - 2021

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N2 - 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.

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 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.

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KW - Homological stability

KW - Brauer algebras

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JO - Selecta Mathematica

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SN - 1022-1824

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The homology of the Brauer algebras

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Keywords

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