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

Dimitri Gurevich; Pavel Saponov

Banach Center Publications (2011)

- Volume: 93, Issue: 1, page 145-162
- ISSN: 0137-6934

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topDimitri 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 -

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