Reflection Equation, Twist, and Equivariant Quantization

Details Reflection Equation, Twist, and Equivariant Quantization Reflection Equation, Twist, and Equivariant Quantization

2002-04-24

arxiv.org/abs/math/0204295v1

Isr. J. Math. V.136 (2003), 11-28

Mathematics

Quantum Algebra

17 pages, AMS Latex

Scientific paper

We prove that the reflection equation (RE) algebra $\La_R$ associated with a finite dimensional representation of a quasitriangular Hopf algebra $\Ha$ is twist-equivalent to the corresponding Faddeev-Reshetikhin-Takhtajan (FRT) algebra. We show that $\La_R$ is a module algebra over the twisted tensor square \twist{$\Ha$}{$\Ha$} and the double $\D(\Ha)$. We define FRT- and RE-type algebras and apply them to the problem of equivariant quantization on Lie groups and matrix spaces.

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