Stable homology isomorphisms for the partition and Jones annular algebras

2023/08/06 by Boyde, Guy · 1 citation
#16E40 #20J06 (Primary) 20B30 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2308.03214

Abstract

We show that the homology of the Jones annular algebras is isomorphic to that of the cyclic groups below a line of gradient (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.

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