Developments and Retrospectives in Lie Theory

Abstract

We define and study a noncommutative Fourier transform on every homogeneous complex bounded domain. We then give an application in noncommutative differential geometry by defining noncommutative Baumslag-Solitar tori.

Noncommutative supergeometry and quantum supergroups

“…This was also recently extended to (non-Abelian) Kählerian Lie groups [32,33] and to the case of SL(2, R) [34] and of SU (1, n) [35]. Star-exponentials [36,37] associated to these deformations were computed in the non-formal setting in [38,39] and such deformations were linked to Hilbert algebras and multipliers in [40]. Non-formal deformation quantization was also extended to the complex case [41,42] and to Abelian p-adic groups [43].…”