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

TL;DR

This paper explicitly computes the Hochschild and cyclic (co)homology of the Fomin-Kirillov algebra on three generators, revealing detailed algebraic structures and dependencies on field characteristics.

Contribution

It provides the first explicit calculations of Hochschild and cyclic (co)homology for this algebra, including the algebra structure of Hochschild cohomology.

Findings

Hochschild (co)homology computed for characteristic not 2 or 3

Cyclic (co)homology obtained in characteristic zero

Algebra structure of Hochschild cohomology determined

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.