dorsal/arxiv
View SchemaSymmetric spaces, non-formal star products and Drinfel'd twists
| Authors | Pierre Bieliavsky |
|---|---|
| Categories | |
| ArXiv ID | 2601.10456vv1 |
| URL | https://arxiv.org/abs/2601.10456 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
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 Math\'ematiques 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 Poincar\'e 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 \'echet algebras from the non-formal noncommutative symmetric spaces defined in the first part.
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"abstract": "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\u0027\u0027 to be held from 7 April to 11 April 2025 at the Centre International de Rencontres Math\\\u0027ematiques 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 Poincar\\\u0027e group (non-metric). In a second part, I explain how to derive non-formal Drinfel\u0027d twists for actions of non-Abelian solvable Lie groups (non-Abelian Universal Deformation Formulae) on or Fr \\\u0027echet algebras from the non-formal noncommutative symmetric spaces defined in the first part.",
"arxiv_id": "2601.10456",
"authors": [
"Pierre Bieliavsky"
],
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"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Symmetric spaces, non-formal star products and Drinfel\u0027d twists",
"url": "https://arxiv.org/abs/2601.10456",
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