Cyclic homology of braided Hopf crossed products

Details Cyclic homology of braided Hopf crossed products Cyclic homology of braided Hopf crossed products

2011-07-05

arxiv.org/abs/1107.0951v1

Mathematics

K-Theory and Homology

63 pages

Scientific paper

Let k be a field, A a unitary associative k-algebra and V a k-vector space endowed with a distinguished element 1_V. We obtain a mixed complex, simpler that the canonical one, that gives the Hochschild, cyclic, negative and periodic homology of a crossed product E:=A#_f V, in the sense of Brzezinski. We actually work in the more general context of relative cyclic homology. Specifically, we consider a subalgebra K of A that satisfies suitable hypothesis and we find a mixed complex computing the Hochschild, cyclic, negative and periodic homology of E relative to K. Then, when E is a cleft braided Hopf crossed product, we obtain a simpler mixed complex, that also gives the Hochschild, cyclic, negative and periodic homology of E.

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