Simplicial Hochschild cochains as an Amitsur complex

Details Simplicial Hochschild cochains as an Amitsur complex Simplicial Hochschild cochains as an Amitsur complex

2007-11-23

arxiv.org/abs/0711.3738v1

Mathematics

Rings and Algebras

5 pages formatted for AGMF proceedings

Scientific paper

It is shown that the cochain complex of relative Hochschild A-valued cochains of a depth two extension A | B under cup product is isomorphic as a differential graded algebra with the Amitsur complex of the coring S = End {}_BA_B over the centralizer R = A^B with grouplike element 1_S, which itself is isomorphic to the Cartier complex of S with coefficients in the (S,S)-bicomodule R^e. This specializes to finite dimensional algebras, H-separable extensions and Hopf-Galois extensions.

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