R-Matrix Poisson Algebras and Their Deformations

Abstract

We classify in this paper Poisson structures on modules over semisimple Lie algebras arising from classical r-matrices. We then study their quantizations and the relation to classical invariant theory.

50 pages

References in corpus (3)

• Deformation quantization of Poisson manifolds, I
• $q$-Wedge Modules for Quantized Enveloping Algebras of Classical Type
• Nichols-Woronowicz algebra model for Schubert calculus on Coxeter groups