Quasi, twisted, and all that... in Poisson geometry and Lie algebroid theory
Abstract
Motivated by questions from quantum group and field theories, we review structures on manifolds that are weaker versions of Poisson structures, and variants of the notion of Lie algebroid. We give a simple definition of the Courant algebroids and introduce the notion of a deriving operator for the Courant bracket of the double of a protobialgebroid. We then describe and relate the various quasiPoisson structures, which have appeared in the literature since 1991, and the twisted Poisson structures studied by Severa and Weinstein.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2003
 arXiv:
 arXiv:math/0310359
 Bibcode:
 2003math.....10359K
 Keywords:

 Mathematics  Symplectic Geometry;
 17B62;
 17B63;
 53D17;
 58A50;
 16W30
 EPrint:
 26 pages