The homology of the Brauer algebras

Rachael Boyd ^[1] ; Richard Hepworth ^[2] ; Peter Patzt ^[3]
1. [1] Max Planck Institute for Mathematics
  
  Max Planck Institute for Mathematics
  
  Kreisfreie Stadt Bonn, Alemania
2. [2] University of Aberdeen
  
  University of Aberdeen
  
  Reino Unido
3. [3] University of Copenhagen, Dinamarca; University of Oklahoma, USA
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Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 5, 2021
Idioma: inglés
DOI: 10.1007/s00029-021-00697-4
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Resumen
- 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.