Coactions on Hochschild Homology of Hopf-Galois Extensions and Their Coinvariants

Details Coactions on Hochschild Homology of Hopf-Galois Extensions and Their Coinvariants Coactions on Hochschild Homology of Hopf-Galois Extensions and Their Coinvariants

2008-10-29

arxiv.org/abs/0810.5326v2

Mathematics

K-Theory and Homology

Version v2: substantially revised. Title changed. To appear in the Journal of Pure and Applied Algebra

Scientific paper

Let A be an H-Galois extension of B. If M is a Hopf bimodule then HH.(A,M), the Hochschild homology of A with coefficients in M, is a right comodule over the coalgebra C:=H/[H,H]. Given an injective left C-comodule V, we denote the cotensor product of M and V by N. Our aim is to investigate the relationship between the cotensor product of HH.(A,M) and V, on the one hand, and HH.(B,N) on the other hand. The roots of this problem can be found in Lorenz's work on the descent of Hochschild homology of centrally Galois extensions, where HH.(A)^G, the subspace of invariant cycles with respect to the action of the Galois group, and HH.(B) are shown to be isomorphic.

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