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

Dimitri Gurevich, and Pavel Saponov. "Quantization of pencils with a gl-type Poisson center and braided geometry." Banach Center Publications 93.1 (2011): 145-162. <http://eudml.org/doc/286222>.

@article{DimitriGurevich2011,
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.},
author = {Dimitri Gurevich, Pavel Saponov},
journal = {Banach Center Publications},
keywords = {Poisson pencil; Poisson center; reflection equaton algebra; super-orbit; Cayley-Hamilton identity; eigenvalues of the generating matrix},
language = {eng},
number = {1},
pages = {145-162},
title = {Quantization of pencils with a gl-type Poisson center and braided geometry},
url = {http://eudml.org/doc/286222},
volume = {93},
year = {2011},
}

TY - JOUR
AU - Dimitri Gurevich
AU - Pavel Saponov
TI - Quantization of pencils with a gl-type Poisson center and braided geometry
JO - Banach Center Publications
PY - 2011
VL - 93
IS - 1
SP - 145
EP - 162
AB - 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.
LA - eng
KW - Poisson pencil; Poisson center; reflection equaton algebra; super-orbit; Cayley-Hamilton identity; eigenvalues of the generating matrix
UR - http://eudml.org/doc/286222
ER -