Braided Gelfand-Zetlin algebras and their semiclassical counterparts
Dimitry Gurevich, Pavel Saponov
TL;DR
This paper constructs braided Gelfand-Zetlin algebras within Reflection Equation algebras linked to Hecke symmetries, especially from quantum groups, and describes their semiclassical Poisson counterparts.
Contribution
It introduces braided Gelfand-Zetlin algebras in Reflection Equation algebras and characterizes their semiclassical Poisson analogs, extending the algebraic framework related to quantum groups.
Findings
Construction of braided Gelfand-Zetlin algebras in Reflection Equation algebras.
Description of semiclassical Poisson counterparts of these algebras.
Connection established between quantum group symmetries and algebraic structures.
Abstract
We construct analogs of the Gelfand-Zetlin algebras in the Reflection Equation algebras, corresponding to Hecke symmetries, mainly to those coming from the quantum groups U_q(sl(N)). Corresponding semiclassical (i.e. Poisson) counterparts of the Gelfand-Zetlin algebras are described.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Operator Algebra Research