The homology of the Brauer algebras

@article{Boyd2021TheHO,
  title={The homology of the Brauer algebras},
  author={Rachael Boyd and Richard A. Hepworth and Peter Patzt},
  journal={Selecta Mathematica},
  year={2021}
}
This paper investigates the homology of the Brauer algebras, interpreted as appropriate $${{\,\mathrm{Tor}\,}}$$ 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 $$\delta $$ 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 $$\delta $$ δ is not invertible, this isomorphism still holds in a… Expand

Figures from this paper

On the homology of the Temperley-Lieb algebras
This paper studies the homology and cohomology of the Temperley-Lieb algebra TL_n(a), interpreted as appropriate Tor and Ext groups. Our main result applies under the common assumption thatExpand
Representation stability for diagram algebras
We introduce stability categories for diagram algebras---analogues to Randal-Williams and Wahl's homogeneous categories. We use these to study representation stability properties of theExpand

References

SHOWING 1-10 OF 52 REFERENCES
Homological stability for Temperley-Lieb algebras
This paper studies the homology and cohomology of the Temperley-Lieb algebra TL_n(a), interpreted as appropriate Tor and Ext groups. Our main result applies under the common assumption thatExpand
Homological stability for the mapping class groups of non-orientable surfaces
We prove that the homology of the mapping class groups of non-orientable surfaces stabilizes with the genus of the surface. Combining our result with recent work of Madsen and Weiss, we obtain thatExpand
Homological stability for Iwahori-Hecke algebras
We show that the Iwahori-Hecke algebras H_n of type A_{n-1} satisfy homological stability, where homology is interpreted as an appropriate Tor group. Our result precisely recovers Nakaoka'sExpand
Homology stability for outer automorphism groups of free groups
We prove that the quotient map from Aut(Fn) to Out(Fn) induces an isomorphism on homology in dimension i for n at least 2i + 4. This corrects an earlier proof by the first author and significantlyExpand
HOMOLOGICAL STABILITY FOR UNORDERED CONFIGURATION SPACES
This paper consists of two related parts. In the first part we give a self-contained proof of homological stability for the spaces C_n(M;X) of configurations of n unordered points in a connected openExpand
Homology stability for linear groups
SummaryLetR be a commutative finite dimensional noetherian ring or, more generally, an associative ring which satisfies one of Bass' stable range conditions. We describe a modified version of H.Expand
Homology stability of $GL_n$ of a Dedekind domain
are isomorphisms for n sufficiently large. This problem has been of particular interest to ^-theorists since K((A) = Ui(BGL (A)) where BGL(A) is a topological space with the property that H*(BGL(A))Expand
Homology stability for the general linear group
This thesis studies the homology stability problem for general linear groups over Euclidean rings and over subrings of the field of rational numbers. Affine linear groups, acting on affine spaceExpand
Representation theory and homological stability
Abstract We introduce the idea of representation stability (and several variations) for a sequence of representations V n of groups G n . A central application of the new viewpoint we introduce hereExpand
Stability of the homology of the mapping class groups of orientable surfaces
The mapping class group of F = Fgs r is F = rgs = wo(A) where A is the topological group of orientation preserving diffeomorphisms of F which are the identity on dF and fix the s punctures. When r =Expand
...
1
2
3
4
5
...