Stable homology isomorphisms for the partition and Jones annular algebras

Abstract

We show that the homology of the Jones annular algebras is isomorphic to that of the cyclic groups below a line of gradient $\frac{1}{2}$. We also show that the homology of the partition algebras is isomorphic to that of the symmetric groups below a line of gradient 1, strengthening a result of Boyd-Hepworth-Patzt. Both isomorphisms hold in a range exceeding the stability range of the algebras in question. Along the way, we prove the usual odd-strand and invertible parameter results for the Jones annular algebras.

20 pages, accepted version

References in corpus (4)

• Homological stability for Iwahori-Hecke algebras of type B
• The homology of a Temperley-Lieb algebra on an odd number of strands
• The homology of the partition algebras
• Idempotents and homology of diagram algebras