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Reflection Equation Algebra and its applications to Noncommutative Geometry

Abstract : Reflection Equation Algebra (REA) is one of the central objects of Braided Geometry. By Braided Geometry I mean a theory related to a braiding, i.e. a solution to the Quantum Yang-Baxter Equation. I’ll exhibit properties of the REA related to different types of braidings. Also, I’ll explain the role of the REA in constructing a differential calculus on the enveloping algebra U(gl(n)). In the case n=2 this calculus leads to a noncommutative version of the Minkowski space algebra. Many of dynamical models of Physics can be generalized to this algebra. A very amusing fact is that these models are in a sense discrete.
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Submitted on : Tuesday, March 2, 2021 - 8:39:02 AM
Last modification on : Tuesday, October 19, 2021 - 6:38:17 PM

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  • HAL Id : hal-03155704, version 1

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Dimitri Gurevich. Reflection Equation Algebra and its applications to Noncommutative Geometry. algebrabelfast2013 : Algebra, Combinatorics, Dynamics and Applications, Sep 2013, Belfast, Ireland. pp.228-253. ⟨hal-03155704⟩

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