Star products and quantization of Poisson-Lie groups

DOI10.1016/0393-0440(92)90035-YzbMath0761.58021OpenAlexW2034646373WikidataQ115363123 ScholiaQ115363123MaRDI QIDQ1200671

Luis Valero, Carlos S. Moreno

Publication date: 16 January 1993

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(92)90035-y

zbMATH Keywords

solutionsquantum groupstriangular quantum Yang-Baxter equation

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Geometric quantization (53D50)

Related Items

Weyl quantization and star products, Deformational quantization of Poisson structures, Invariant star-product on a Poisson-Lie group and \(h\)-deformation of the corresponding Lie algebra, Bialgebra actions, twists, and universal deformation formulas

Cites Work

• The local structure of Poisson manifolds
• Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds
• Compact matrix pseudogroups
• Geodesic symmetries and invariant star products on Kähler symmetric spaces
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• Déformations d'algèbres associées à une variété symplectique (les \(*_\nu\)-produits)
• Déformation du crochet de Poisson sur une variété symplectique
• Deformation theory and quantization. II: Physical applications
• Deformation quantization of Heisenberg manifolds
• Invariant star products and representations of compact semisimple Lie groups
• On the deformation of rings and algebras
• Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures
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