Quantization of pencils with a $gl$-type Poisson center and braided geometry
Volume 93 / 2011
Banach Center Publications 93 (2011), 145-162
MSC: Primary 81R60; Secondary 81S10.
DOI: 10.4064/bc93-0-12
Abstract
We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson pencils and describe the corresponding quantum algebras. A few detailed examples are exhibited.
