Hochschild (co)homology of Hopf crossed products

Details Hochschild (co)homology of Hopf crossed products Hochschild (co)homology of Hopf crossed products

2001-04-06

arxiv.org/abs/math/0104075v1

Mathematics

K-Theory and Homology

26 pages

Scientific paper

Let A a k-algebra, H a Hopf algebra, E = A#H a general crossed product and M an E-bimodule. We obtain a complex simpler than the canonical one, giving the Hochschild homology of E with coefficients in M. This complex is eqquiped with a natural filtration. We prove that the associated spectral sequence coincides with that obtained by either, the Hochschild-Serre direct method or the Cartan-Leray-Grothendieck method. We also get similar results for the cohomology.

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