Hochschild cohomology and stratifying ideals.
Given an algebra \(B\) and a stratifying ideal \(I=BeB\) of \(B\), where \(e\) is an idempotent generating \(I\), the authors establish a long exact sequence relating the Hochschild cohomology groups of the algebras \(B\), \(B/I\) and \(eBe\). This generalizes many results in the literature. The authors also study the quotient of the Hochschild cohomology algebra modulo the ideal generated by all homogeneous nilpotent elements. The authors show that such quotient for \(B\) embeds (as a graded algebra) into the product of the corresponding quotients for \(B/I\) and \(eBe\). Using this it is proved that such quotient is finitely generated in the case of the Brauer algebra \(B_k(3,\delta)\), verifying in this case a conjecture of Snashall and Solberg. Finally, the authors consider a condition under which the mentioned quotients for the algebras \(B\) and \(eBe\) are isomorphic.
scientific article; zbMATH DE number 5527507