Hochschild and cyclic (co)homology of the Fomin–Kirillov algebra on $3$ generators

Abstract

The goal of this article is to explicitly compute the Hochschild (co)homology of the Fomin–Kirillov algebra on three generators over a field of characteristic different from $2$ and $3$. We also obtain the cyclic (co)homology of the Fomin–Kirillov algebra in case the characteristic of the field is zero. Moreover, we compute the algebra structure of the Hochschild cohomology.