Quantization of semisimple real Lie groups

Kenny De Commer

Address: Department of Mathematics and Data Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium

E-mail: kenny.de.commer@vub.be

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.

AMSclassification: primary 17B37; secondary 20G42, 46L67.

Keywords: quantum groups, real forms, quantized enveloping algebras, Harish-Chandra modules.

DOI: 10.5817/AM2024-5-285