Hochschild and ordinary cohomology rings of small categories
By Fei Xu. 2008
76 citations recorded by the source corpus.
Let be a small category and k a field. There are two interesting mathematical subjects: the category algebra and the classifying space . We study the ring homomorphism and prove it is split surjective, using the factorization category of Quillen [D. Quillen, Higher algebraic K-theory I, in: Lecture Notes in Math., vol. 341, Springer-Verlag, Berlin, 1973, pp. 85�147] and certain techniques from functor cohomology theory. This generalizes the well-known theorems 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, disproving a conjecture of Snashall and Solberg [N. Snashall, O. Solberg, Support varieties and Hochschild cohomology rings, Proc. London Math. Soc. 88 (3) (2004) 705�732].
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9f53ba1343971bdf3933384e0b0895085f763ed4
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In Discrete Mathematics and Combinatorics
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Citations in the corpus
- The hochschild cohomology ring of a class of special biserial algebras (2008, background): “It is known that the conjecture is not true in general (see [24] in which the author gives a counter-example which is a 7-dimensional Koszul algebra that is not self-injective).”