Noncommutative Geometry and Topology in Prague

Quantization of linear real semisimple Lie groups

Let L be a connected linear real semisimple Lie group, with associated real semisimple Lie algebra l. We present a novel construction of a *-algebra quantizing the universal enveloping *-algebra of l, and then show how this *-algebra can be `integrated’ into a C*-algebra which quantizes the universal group C*-algebra of L.  Our construction builds on Letzter’s theory of coideal subalgebras of quantized enveloping algebras, coming from the classical theory of symmetric spaces (of compact type).