Simplicial Hochschild cochains as an Amitsur complex
Abstract
It is shown that the cochain complex of relative Hochschild Avalued 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, Hseparable extensions and HopfGalois extensions.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.3738
 Bibcode:
 2007arXiv0711.3738K
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  KTheory and Homology;
 18G25
 EPrint:
 5 pages formatted for AGMF proceedings