Happel's question, Han's conjecture and $\tau$-Hochschild (co)homology

Abstract

We introduce the $\tau$-Hochschild (co)homology of a finite dimensional associative algebra $\Lambda$ by means of the higher Auslander-Reiten translate of O. Iyama. We show that the global dimension of $\Lambda$, Happel's question and Han's conjecture are related to the $\tau$-Hochschild (co)homology.

27 pages, minor changes. To appear in Annals of K-Theory