An exceptional splitting of Khovanov’s arc algebras in characteristic 2
Volume 264 / 2024
Fundamenta Mathematicae 264 (2024), 69-84
MSC: Primary 57K18; Secondary 57K16, 16D20, 16W50
DOI: 10.4064/fm230712-2-12
Published online: 27 March 2024
Abstract
We show that there is an associative algebra $\widetilde H_n$ such that, over a base ring $R$ of characteristic 2, Khovanov’s arc algebra $H_n$ is isomorphic to the algebra $\widetilde H_n[x]/(x^2)$. We also show a similar result for bimodules associated to planar tangles and prove that there is no such isomorphism over $\mathbb Z$.
