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

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