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

Abstract

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