Hochschild and ordinary cohomology rings of small categories

Details Hochschild and ordinary cohomology rings of small categories Hochschild and ordinary cohomology rings of small categories

2008-05-21

arxiv.org/abs/0805.3295v2

Mathematics

Algebraic Topology

Advances in Mathematics, to appear

Scientific paper

Let C be a small category and k a field. There are two interesting mathematical subjects: the category algebra kC and the classifying space |C|=BC. We study the ring homomorphism HH*(kC) --> H*(|C|,k) and prove it is split surjective. This generalizes the well-known results for groups and posets. Based on this result, we construct a seven-dimensional category algebra whose Hochschild cohomology ring modulo nilpotents is not finitely generated, against a conjecture of Snashall and Solberg.

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