%0 Journal Article
%T Cohomology of split algebras and of trivial extensions
%A Claude Cibils
%A Eduardo Marcos
%A Maria Julia Redondo
%A Andrea Solotar
%J Mathematics
%D 2001
%I arXiv
%X We consider associative algebras L over a field provided with a direct sum decomposition of a two-sided ideal M and a sub-algebra A - examples are provided by trivial extensions or triangular type matrix algebras. In this relative and split setting we describe a long exact sequence computing the Hochschild cohomology of L. We study the connecting homomorphism using the cup-product and we infer several results, in particular the first Hochschild cohomology group of a trivial extension never vanishes.
%U http://arxiv.org/abs/math/0102194v5