Homology, Homotopy and Applications

Volume 4 (2002)

Number 2

The Roos Festschrift volume

Crossed extensions of algebras and Hochschild cohomology

Pages: 63 – 82

DOI: https://dx.doi.org/10.4310/HHA.2002.v4.n2.a4


Hans-Joachim Baues (Max-Planck-Institut für Mathematik, Bonn, Germany)

Elias Gabriel Minian (Max-Planck-Institut für Mathematik, Bonn, Germany)


We introduce the notion of crossed $n$-fold extensions of an algebra $B$ by a bimodule $M$ and prove that such extensions represent classes in the Hochschild cohomology of $B$ with coefficients in $M$. Moreover we consider this way characteristic classes of chain (resp. cochain) algebras in Hochschild cohomology.


Hochschild cohomology, Massey products, crossed module

2010 Mathematics Subject Classification


Published 1 January 2002