Quantization of Poisson pencils and generalized Lie algebras

DOI10.1007/BF02065870zbMath0855.58032arXivq-alg/9501007OpenAlexW2089840130MaRDI QIDQ1920645

Vladimir Rubtsov, Dimitri Gurevich

Publication date: 12 August 1996

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9501007

zbMATH Keywords

quantizationquantum algebrasgeneralized Lie algebrasPoisson pencils

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Infinite-dimensional Lie (super)algebras (17B65) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geometric quantization (53D50)

Related Items (2)

Compatible Poisson brackets, quadratic Poisson algebras and classical r-matrices ⋮ Double quantization of \(\mathbb{C}\mathbb{P}^n\) type orbits by generalized Verma modules

Cites Work

• What is a classical r-matrix?
• Representation-functors and flag-algebras for the classical groups. I
• Quantization of Poisson pairs: The \(R\)-matrix approach
• On Poisson pairs associated to modified \(R\)-matrices
• Quantum and braided-Lie algebras
• Quasi-associativity and flatness criteria for quadratic algebra deformations
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Quantum orbits of the \(R\)-matrix type
• Poincaré-Birkhoff-Witt theorem for quadratic algebras of Koszul type
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