Daniel Beltita

Quantization and enveloping algebras of Lie groups

We discuss associative algebras whose representations can be used for parameterizing the representations of a given Lie group, with emphasis on the algebra of invariant differential operators and on the group $C^*$-algebra. Special attention is paid to the question of whether certain Lie groups can be recovered from their corresponding associative algebras. We also consider the way these associative algebras are related to the canonical Poisson structures on the dual spaces of the Lie algebras under consideration, which bears on the construction of Lie group representations by the method of geometric quantization.

XXXIX Workshop on Geometric Methods in Physics	19.06–25.06.2022
XI School on Geometry and Physics	27.06–1.07.2022

Event sponsored by:
University of Bialystok