Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.10456 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- These notes refer to a minicourse I gave at the occasion of the conference meeting ``Applications of Noncommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time'' to be held from 7 April to 11 April 2025 at the Centre International de Rencontres Mathématiques in Luminy. They consist in a review of a long standing work of mine and collaborators (see references therein) in the field of non-formal deformation quantization admitting a large group of symmetries. But they also contain new material and results. More precisely, in a first part, I present a method (called the Retract Method) to define quantizations/symbolic calculi and associated operator symbol composition formulae (non-formal deformations/star products) of symplectic symmetric spaces such as the hyperbolic plane (Kahler) or symmetric co-adjoint orbits of the Poincaré group (non-metric). In a second part, I explain how to derive non-formal Drinfel'd twists for actions of non-Abelian solvable Lie groups (non-Abelian Universal Deformation Formulae) on or Fr échet algebras from the non-formal noncommutative symmetric spaces defined in the first part.