Cohomology of split algebras and of trivial extensions

Details Cohomology of split algebras and of trivial extensions Cohomology of split algebras and of trivial extensions

2001-02-26

arxiv.org/abs/math/0102194v5

Mathematics

K-Theory and Homology

Scientific paper

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.

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