Symmetric spaces, non-formal star-products and Drinfel’d twists
(2026) EMS Series of Lectures in Mathematics — ISBN: [9783985471089], 213-313, published
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- Authors
Bieliavsky, Pierre 
- Abstract
- These notes present old and new results of mine and collaborators in the field of non-formal deformation quantization of symplectic symmetric spaces. I first review an explicit construction of oscillatory integral formulae for symmetry-invariant non-formal star-products on symplectic symmetric spaces. In a second step, I present a method for explicitly constructing non-formal invariant star-products on a large class of homogeneous symplectic spaces. In a third step, I review a joint work with V. Gayral where we explicitly define non-formal universal deformation formulae (Drinfel’d twists) for actions of non-Abelian Lie groups. At last, I present a class of symmetry-invariant non-formal star-product function algebras on the hyperbolic plane. These algebras are represented by sub-∗-algebras of compact operators acting in the projective holomorphic discrete series of SL(2,R).
- Affiliations
Citations
Bieliavsky, P. (2026). Symmetric spaces, non-formal star-products and Drinfel’d twists. In Ali H. Chamseddine, Alain Connes, Masoud Khalkhali, Joseph Kouneiher (ed.), EMS Series of Lectures in Mathematics (pp. 213-313). EMS Press. https://doi.org/10.4171/ELM/37/6