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arXiv · 2308.03214

Stable homology isomorphisms for the partition and Jones annular algebras

Guy Boyde
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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.

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Guy Boyde. 2023-08-06. Stable homology isomorphisms for the partition and Jones annular algebras. https://doi.org/10.1007/s00029-024-00992-w

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