On Poisson pairs associated to modified \(R\)-matrices

DOI10.1215/S0012-7094-94-07311-0zbMath0824.58022OpenAlexW2047685394MaRDI QIDQ1325161

Dmitri I. Panyushev, Dimitri Gurevich

Publication date: 9 November 1995

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-94-07311-0

zbMATH Keywords

homogeneous spacesPoisson brackets\(R\)-matrix

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Differential geometry of homogeneous manifolds (53C30) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (8)

Quantum symmetric spaces ⋮ Quasi-associativity and flatness criteria for quadratic algebra deformations ⋮ Unnamed Item ⋮ Quantum orbits of the \(R\)-matrix type ⋮ Quantization of Poisson pencils and generalized Lie algebras ⋮ On the geometric quantization of \(R\)-matrix-type Poisson brackets ⋮ Double quantization of \(\mathbb{C}\mathbb{P}^n\) type orbits by generalized Verma modules ⋮ Poisson Homology of r-Matrix Type Orbits I: Example of Computation

Cites Work

• Unnamed Item
• Unnamed Item
• Some remarks on nilpotent orbits
• Quantization of Poisson pairs: The \(R\)-matrix approach
• Complexity and nilpotent orbits
• A family of Poisson structures on Hermitian symmetric spaces
• Some Poisson structures associated to Drinfeld-Jimbo \(R\)-matrices and their quantization
• Solutions of the classical Yang-Baxter equation for simple Lie algebras

This page was built for publication: On Poisson pairs associated to modified \(R\)-matrices