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.
Categories: math.AT math.GT math.RT