Quantum orbits of R-matrix type

Abstract

Given a simple Lie algebra $\gggg$, we consider the orbits in $\gggg^*$ which are of R-matrix type, i.e., which possess a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the so-called R-matrix bracket. We call an algebra quantizing the latter bracket a quantum orbit of R-matrix type. We describe some orbits of this type explicitly and we construct a quantization of the whole Poisson pencil on these orbits in a similar way. The notions of q-deformed Lie brackets, braided coadjoint vector fields and tangent vector fields are discussed as well.

18 pp., Latex

References in corpus (2)

• Free Braided Differential Calculus, Braided Binomial Theorem and the Braided Exponential Map
• Quantum and Braided Lie Algebras

Cited by in corpus (3)

• Double quantization of $\cp$ type orbits by generalized Verma modules
• Quantization of Poisson pencils and generalized Lie algebras
• Some aspects of braided geometry: differential calculus, tangent space, gauge theory