Quantisation of semisimple real Lie groups

Abstract

We provide a novel construction of quantized universal enveloping $\ast$-algebras of real semisimple Lie algebras, based on Letzter's theory of quantum symmetric pairs. We show that these structures can be `integrated', leading to a quantization of the group C${}^{\ast }$-algebra of an arbitrary semisimple algebraic real Lie group.

21 pages. For submission to the conference proceedings of the Conference `Quantum Groups and Noncommutative Geometry' (Prague, 2023)