The homology of the Brauer algebras

Rachel Boyd, Richard Hepworth, Peter Patzt

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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 languageEnglish
Article number85
Number of pages31
JournalSelecta Mathematica
Issue number5
Early online date25 Aug 2021
Publication statusPublished - 2021


  • Homology
  • Homological stability
  • Brauer algebras


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