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

• Autorzy: Dimitri Gurevich , Pavel Saponov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 81R60: Noncommutative geometry
• 81S10: Geometry and quantization, symplectic methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 93
• Numer: 1
• Strony: 145-162

Daty

wydano

2011

Twórcy

autor

Dimitri Gurevich

• LAMAV, Université de Valenciennes, 59313 Valenciennes, France

autor

Pavel Saponov

• Division of Theoretical Physics, Institute for High Energy Physics, 142284 Protvino, Russia

Identyfikatory

DOI

10.4064/bc93-0-12