Homology of Epsilon-Strongly Graded Algebras

Abstract

Let $G$ be a group and $S$ a unital epsilon-strongly $G$-graded algebra. We construct spectral sequences converging to the Hochschild (co)homology of $S$. Each spectral sequence is expressed in terms of the partial group (co)homology of $G$ with coefficients in the Hochschild (co)homology of the degree-one component of $S$. Moreover, we show that the homology spectral sequence decomposes according to the conjugacy classes of $G$, and, by means of the globalization functor, its $E^2$-page can be identified with the ordinary group homology of suitable centralizers.