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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-12,
author = {Dimitri Gurevich and Pavel Saponov},
title = {Quantization of pencils with a gl-type Poisson center and braided geometry},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {145-162},
zbl = {1248.81090},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-12}
}
Dimitri Gurevich; Pavel Saponov. Quantization of pencils with a gl-type Poisson center and braided geometry. Banach Center Publications, Tome 95 (2011) pp. 145-162. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-12/