Representation Theory and Noncommutative Geometry, Paris

First-order differential calculi and Laplacians on q-deformations of compact semisimple Lie groups

11 févr. 2025, 15:00

45m

Amphitheater Darboux (IHP)

Orateur

Dr Heon Lee (Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China)

Description

In this talk, we suggest a simple definition of Laplacian on a compact quantum group (CQG) associated with a first-order differential calculus (FODC) on it. Applied to the classical differential calculus on a compact Lie group, this definition yields classical Laplacians, as it should. Moreover, on the CQG $K_q$ arising from the $q$-deformation of a compact semisimple Lie group $K$, we can find many interesting linear operators that satisfy this definition, which converge to a classical Laplacian on $K$ as $q$ tends to 1. In light of this, we call them $q$-Laplacians on $K_q$ and investigate some of their operator theoretic properties. This work is based on the preprint arXiv:2410.00720.