Michel NGUIFFO BOYOM
UNIVERSITE MONTPELLIER2 (FRANCE)
boyom@math.univ-montp2.fr

Coauthors: Robert WOLAK


Local structure of Koszul-Vinberg algebroids and Lie algebroids

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 .