Quantization of pencils with a gl-type Poisson center and braided geometry
Quantum Algebra
2010-02-09 v1
Abstract
In the algebra Sym(gl(m)) we consider Poisson pencils generated by the linear Poisson-Lie bracket {,}_{gl(m)} and that corresponding to the so-called Reflection Equation Algebra. Each bracket of such a pencil has the Poisson center coinciding with that of the bracket {,}_{gl(m)}. Consequently, any bracket from this pencil can be restricted to a generic GL(m)-orbit O in gl(m)*. Quantization of such a restricted bracket can be done in the frameworks of braided affine geometry. In the paper we consider these Poisson structures, their super-analogs as well as their quantum (braided) counterparts. Also, we exhibit some detailed examples.
Keywords
Cite
@article{arxiv.1002.1594,
title = {Quantization of pencils with a gl-type Poisson center and braided geometry},
author = {D. I. Gurevich and P. A. Saponov},
journal= {arXiv preprint arXiv:1002.1594},
year = {2010}
}