Cohomology of products and coproducts of augmented algebras

Details Cohomology of products and coproducts of augmented algebras Cohomology of products and coproducts of augmented algebras

2010-07-23

arxiv.org/abs/1007.4110v1

Mathematics

Representation Theory

14 pages

Scientific paper

We show that the ordinary cohomology functor from the category of augmented $k$-algebras to itself exchanges coproducts and products, and that Hochschild cohomology is close to sending coproducts to products if the factors are self-injective. We identify the multiplicative structure of the Hochschild cohomology of a product modulo a certain ideal in terms of the cohomology of the factors.

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