제목: Quantum Holomorphic Evaluations and the Universal Property of Complex Semisimple Quantum Groups

초록: The first example of a q-deformed complex semisimple Lie group—the quantum Lorentz group introduced by Podleś and Woronowicz (1990)—was defined as a universal $C^*$-algebra given by affiliated unbounded generators and relations. Although this q-deformation was later extended to all complex semisimple quantum groups, the original universal property in terms of generators and relations—the very motivation for introducing complex semisimple quantum groups—has since disappeared from the literature.

In this talk, we address this gap. Specifically, we provide an equivalent reformulation of the universal property of the quantum Lorentz group and extend it to all complex semisimple quantum groups. We also discuss several semiclassical aspects of these quantum groups.

This talk is based on joint work with Christian Voigt.