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- W2058444534 abstract "Let B⊆A be an H-Galois extension, where H is a Hopf algebra over a field K. 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 CH=H/[H,H]. Given an injective left CH-comodule V, our aim is to understand the relationship between HH∗(A,M)□CHV and HH∗(B,M□CHV). The roots of this problem can be found in Lorenz (1994) [15], where HH∗(A,A)G and HH∗(B,B) are shown to be isomorphic for any centrally G-Galois extension. To approach the above mentioned problem, in the case when A is a faithfully flat B-module and H satisfies some technical conditions, we construct a spectral sequence TorpRH(K,HHq(B,M□CHV))⟹HHp+q(A,M)□CHV, where RH denotes the subalgebra of cocommutative elements in H. We also find conditions on H such that the edge maps of the above spectral sequence yield isomorphisms K⊗RHHH∗(B,M□CHV)≅HH∗(A,M)□CHV. In the last part of the paper we define centrally Hopf–Galois extensions and we show that for such an extension B⊆A, the RH-action on HH∗(B,M□CHV) is trivial. As an application, we compute the subspace of H-coinvariant elements in HH∗(A,M). A similar result is derived for HC∗(A), the cyclic homology of A." @default.
- W2058444534 created "2016-06-24" @default.
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- W2058444534 date "2010-09-01" @default.
- W2058444534 modified "2023-09-27" @default.
- W2058444534 title "Coactions on Hochschild homology of Hopf–Galois extensions and their coinvariants" @default.
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- W2058444534 doi "https://doi.org/10.1016/j.jpaa.2009.12.010" @default.
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