Simplicial Hochschild cochains as an Amitsur complex

2007/11/23 by Lars Kadison, Kadison, Lars
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.0711.3738

Abstract

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.

Related

• Hochschild and Simplicial Cohomology
• Corings, their dual rings and relative (co)Hochschild cohomology
• The Continuous Hochschild Cochain Complex of a Scheme
• Hochschild cochains as a Frobenius algebra
• Gerstenhaber algebra and Deligne's conjecture on Tate-Hochschild cohomology