The cohomology of Koszul–Vinberg algebras

Michel Nguiffo Boyom

Vol. 225 (2006), No. 1, 119–153

DOI: 10.2140/pjm.2006.225.119

Abstract

We study 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 1969. In particular, we completely solve a fundamental problem raised by M. Gerstenhaber. A short appendix is devoted to the relationships between our results and the pioneering work of Nijenhuis.

Keywords

Koszul–Vinberg algebra, KV-module, KV-cohomology, KV-cochain, connection-like coycle

Mathematical Subject Classification 2000

Primary: 55N35, 53B05, 22E65

Secondary: 17A30, 17B60

Milestones

Received: 6 March 2003

Revised: 25 January 2005

Accepted: 15 March 2006

Published: 1 May 2006