Quantisation of semisimple real Lie groups

TL;DR

This paper introduces a new method for quantizing real semisimple Lie groups using quantum symmetric pairs, enabling the construction of their group C*-algebras, thus advancing the mathematical framework of quantum group theory.

Contribution

It presents a novel construction of quantized universal enveloping *-algebras for real semisimple Lie algebras based on Letzter's theory, and demonstrates their integration into group C*-algebras.

Findings

Construction of quantized universal enveloping *-algebras for real semisimple Lie algebras

Integration of these structures into group C*-algebras

Extension of quantum group theory to real semisimple Lie groups

Abstract

We provide a novel construction of quantized universal enveloping $*$-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$^*$-algebra of an arbitrary semisimple algebraic real Lie group.