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

2010/02/08 by Dimitri Gurevich, D. I. Gurevich, Pavel Saponov +3
Mathematics · #81R60 #81S99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA #msc:81R60 #msc:81S99

paper · pdf · doi:10.48550/arxiv.1002.1594

arxiv created 2010/02/08 · openalex publication_date 2010/02/08 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the algebra Sym(gl(m)) we consider Poisson pencils generated by the linear Poisson-Lie bracket ,_gl(m) and that corresponding to the so-called Reflection Equation Algebra. Each bracket of such a pencil has the Poisson center coinciding with that of the bracket ,_gl(m). Consequently, any bracket from this pencil can be restricted to a generic GL(m)-orbit O in gl(m)*. Quantization of such a restricted bracket can be done in the frameworks of braided affine geometry. In the paper we consider these Poisson structures, their super-analogs as well as their quantum (braided) counterparts. Also, we exhibit some detailed examples.

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