Colloque 2013 du GDR 2875, Topologie Algébrique et Applications

Non-commutative algebras and Poisson algebras

17 oct. 2013, 12:00

45m

Amphi L005 (bâtiment L) (Université d'Angers)

Exposé de recherche sur invitation Topologie algébrique et applications

Orateur

Mme Anne Pichereau (ICJ, Univ. Jean Monnet)

Description

This is a joint work with R. Berger (St-Etienne). Following the idea that classical mechanics should be a limit case of quantum mechanics, P.A.M. Dirac explained that the commutator of dynamical variables in quantum mechanics should be the analogue of the symplectic Poisson bracket of |R^{2r} in classical mechanics. Working in a mathematical setting, we consider a non-commutative algebra B, which can be seen as a deformation of a Poisson algebra T. This algebra B belongs to a family of 3-Calabi-Yau algebras defined by potentials and depending on a natural integer n and the algebra B is for us the most interesting example in the case n=2. We give cohomological links between B and T, as we obtain the Poisson cohomology of T and prove that the Hochschild cohomology of B is isomorphic to the Poisson cohomology of T.