HOCHSCHILD COHOMOLOGY AND STRATIFYING IDEALS HIROSHI NAGASE

Abstract. Suppose B is an algebra with a stratifying ideal BeB generated by an idempotent e. We will establish long exact sequences relating the Hochschild cohomology groups of the three algebras B, B=BeB and eBe. This provides a common generalization of various known results, all of which are extending Happel's long exact sequence for one-point extensions. Applying one of these sequences to Hochschild cohomology algebras modulo nilpotent shows, in some cases, that these algebras are ¯nitely generated. 1