Products in Hochschild cohomology and Grothendieck rings of group crossed products

Details Products in Hochschild cohomology and Grothendieck rings of group crossed products Products in Hochschild cohomology and Grothendieck rings of group crossed products

2002-11-30

arxiv.org/abs/math/0212003v1

Mathematics

Rings and Algebras

21 pages

Scientific paper

We give a general construction of rings graded by the conjugacy classes of a finite group. Some examples of our construction are the Hochschild cohomology ring of a finite group algebra, the Grothendieck ring of the Drinfel'd double of a group, and the orbifold cohomology ring for a global quotient. We generalize the first two examples by deriving product formulas for the Hochschild cohomology ring of a group crossed product and for the Grothendieck ring of an abelian extension of Hopf algebras. Our results account for similarities in the product structures among these examples.

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