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