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5-th Conference on Geometry and Topology of Manifolds
April 27 - May 3, 2003

Krynica, Poland

Organizers
Institute of Mathematics of the Technical University of Lodz; Institute of Mathematics of the Jagiellonian University, Cracow; Faculty of Applied Mathematics of the University Mining and Matallurgy, Cracow

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Quadartization of Lie algebroid
by
Michel Nguiffo Boyom
Université Montpellier 2, Montpellier, France

Let \Pi be a smooth Poisson tensor on Rn such that \Pi( 0) = 0. Then, the linear part of the Taylor expansion at 0 of \Pi defnes a Lie algebra structure on the vector space of linear functions on Rn. According to Alan WEINSTEIN, a Lie algebra L is formally (resp. smoothly or analytically) nondegenerate if every Poisson tensor on Rn, say \Pi, which vanishes at 0 and whose linear part at 0 is isomorphic to L is formally (resp. smoothly or analytically) linearizable at 0. By a brupt force, Jean-Paul DUFOUR and Nguen Tien ZUNG recently prove that the algebra aff(n) of affine endomorphisms of Rn is non analytically denegenerate. The aim if this talk is to sketch the proof of the formal nondegenerancy aff(n) and to extend that nondegenerancy property the class of ''AffineLike Lie algebrAs''.

Date received: April 26, 2003

Copyright © 2003 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 # cakm-22.