Simplicial Hochschild cochains as an Amitsur complex 1

Lars KADISON

Abstract

It is shown how the cochain complex of the 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 BAB over the centralizer R = AB with grouplike element 1S. This specializes to finite dimensional algebras, Hopf-Galois extensions and H-separable extensions.