The homology of the Brauer algebras

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

Automated summary

This paper investigates the homology of the Brauer algebras in relation to the symmetric group, showing that they are closely related. The main results demonstrate that the homology of the Brauer algebra is isomorphic to the homology of the symmetric group when the defining parameter delta is invertible, and that this isomorphism holds in a range of degrees that increases with n when delta is not invertible.