Local structure of Koszul-Vinberg algebroids and Lie algebroids
by
Michel Nguiffo Boyom
Universite Montpelier 2 (France)
Coauthors: Robert Wolak

The word manifold is used for smooth or complex analytic manifold .We deal with connected and paracompact manifolds . For a given manifold M F(M, K) stands for the associative K-algebra of K-valued smooth functions if K = R (resp. the sheaf of complex analytic functions if K = C ) . Geometric objects considered on M are either smooth or complex analytic according to K : = R or C . Given a vector bundle A on M sect(A) stands for the F(M, K)-module of sections of A . A Koszul-Vinberg algebroid (resp Lie algebroid ) on M is couple (A, a ) where A is a vector bundle on M and a is a vector bundle M-homomorphism from A to TM (, TM is the holomorphic tangent bundle when K = C , ) such that (i) sect(A) is endoved with a structure of Koszul-Vinberg algebra (sect(A) , . ) (resp. structure of Lie algebra ( sect(A) , [ , ] ) ; (ii) given S , S' in sect(A) and f in F(M, K) one has (fS).S' = f(S.S') and S.(fS') = f(S.S') + (a(S)f)S', (resp. [ fS , S' ] = f[ S , S' ] + (a(S)f)S' . ) The purpose of the confernce is to expose a decomposition theorem ( normal forms ) of KV-algebroids ( resp. Lie algebroids ) and a local classification theorem as well .

Date received: April 15, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajc-11.