Cohomology of split algebras and of trivial extensions

2001/02/26 by Claude Cibils, Cibils, Claude, Eduardo Marcos +8 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.KT #math.RA #msc:16D20 #msc:16E40

paper · pdf · doi:10.48550/arxiv.math/0102194

arxiv created 2002/07/05 · arxiv updated 2009/11/30

Abstract

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.

Cited by

• Hochschild cohomology of triangular matrix algebras

Related

• Hochschild cohomology of relation extension algebras
• Cohomology of trivial extensions of Frobenius algebras
• The Multiplicative Structure on Hochschild Cohomology of a Complete Intersection
• Hochschild cohomology of triangular matrix algebras
• Extensions of associative algebras