Quantization of symplectic dynamical r-matrices and the quantum composition formula

Anton Alekseev (1) , Damien Calaque (2)

1 UNIGE - Université de Genève = University of Geneva
2 MPI - Max-Planck-Institut für Mathematik

In this paper we quantize symplectic dynamical r-matrices over a possibly nonabelian base. The proof is based on the fact that the existence of a star-product with a nice property (called strong invariance) is sufficient for the existence of a quantization. We also classify such quantizations and prove a quantum analogue of the classical composition formula for coboundary dynamical r-matrices.

Domaines: Algèbres quantiques [math.QA]; Physique mathématique [math-ph]

Anton Alekseev, Damien Calaque. Quantization of symplectic dynamical r-matrices and the quantum composition formula. Communications in Mathematical Physics, 2007, 273 (1), pp.119-136. ⟨10.1007/s00220-007-0245-z⟩. ⟨hal-00133166⟩