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

Tom 93 / 2011

Dimitri Gurevich, Pavel Saponov Banach Center Publications 93 (2011), 145-162 MSC: Primary 81R60; Secondary 81S10. DOI: 10.4064/bc93-0-12

Streszczenie

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.

Autorzy

  • Dimitri GurevichLAMAV
    Université de Valenciennes
    59313 Valenciennes, France
    e-mail
  • Pavel SaponovDivision of Theoretical Physics
    Institute for High Energy Physics
    142284 Protvino, Russia
    e-mail

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