The cohomology of Koszul-Vinberg algebras

Abstract

This work is devoted to an intrinsic cohomology theory of Koszul-Vinberg algebras and their modules. Our results may be regarded as improvements of the attempt by Albert Nijenhuis in [NA]. The relationships between the cohomology theory developed here and some classical problems are pointed out, e.g. extensions of algebras and modules, and deformation theory. The real Koszul-Vinberg cohomology of locally flat manifolds is initiated. Thus regarding the idea raised by M. Gerstenhaber we can state : The category of KV-algebras has its proper cohomology theory.