Quantization of pencils with a gl-type Poisson center and braided geometry

Details Quantization of pencils with a gl-type Poisson center and braided geometry Quantization of pencils with a gl-type Poisson center and braided geometry

2010-02-08

arxiv.org/abs/1002.1594v1

Mathematics

Quantum Algebra

Scientific paper

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.

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