Speaker
Mrs
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.
| Mots Clés / Keywords | Poisson and Hochschild (co)homology |
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Primary author
Mrs
Anne Pichereau
(ICJ, Univ. Jean Monnet)
