Hochschild Cohomology of Triangular Matrix Algebras

AbstractWe study the Hochschild cohomology of triangular matrix rings B=R0AMRA , where A and R are finite dimensional algebras over an algebraically closed field K and M is an A-R-bimodule. We prove the existence of two long exact sequences of K-vector spaces relating the Hochschild cohomology of A, R, and B

Presentations of Trivial Extensions of Finite Dimensional Algebras and a Theorem of Sheila Brenner

AbstractLet Λ be a finite dimensional algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of Λ is zero in Λ. We describe the ordinary quiver and relations for T(Λ)=Λ⋉D(Λ), the trivial extension of Λ by its minimal injective cogenerator D(Λ), and also for the repetitive algebra [formula] of Λ. Associated with this description we give an application of a theorem of Sheila Brenner