2 citations · 2 across the 2 of their papers we have counts for
9 papers
The homology of the partition algebras
Rachael Boyd, Richard Hepworth, Peter Patzt
We show that the homology of the partition algebras, interpreted as appropriate Tor-groups, is isomorphic to that of the symmetric groups in a range of degrees that increases with…
Groups of convex bodies
Richard Hepworth
In this paper we introduce and study a topological abelian group of convex bodies, analogous to the scissors congruence group and McMullen's polytope algebra, with the universal pr…
The homology of the Brauer algebras
Rachael Boyd, Richard Hepworth, Peter Patzt
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…
Combinatorics of injective words for Temperley-Lieb algebras
Rachael Boyd, Richard Hepworth
This paper studies combinatorial properties of the 'complex of planar injective words', a chain complex of modules over the Temperley-Lieb algebra that arose in our work on homolog…
The homology of the Temperley-Lieb algebras
Rachael Boyd, Richard Hepworth
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 assump…
Homological stability for Iwahori-Hecke algebras
Richard Hepworth
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…