Duality and self-duality for dynamical quantum groups

Details Duality and self-duality for dynamical quantum groups Duality and self-duality for dynamical quantum groups

2001-07-31

arxiv.org/abs/math/0107225v1

Algebr. Represent. Theory 7 (2004), 363-393

Mathematics

Quantum Algebra

26 pages

Scientific paper

We define a natural concept of duality for the h-Hopf algebroids introduced by Etingof and Varchenko. We prove that the special case of the trigonometric SL(2) dynamical quantum group is self-dual, and may therefore be viewed as a deformation both of the function algebra F(SL(2)) and of the enveloping algebra U(sl(2)). Matrix elements of the self-duality in the Peter-Weyl basis are 6j-symbols; this leads to a new algebraic interpretation of the hexagon identity or quantum dynamical Yang-Baxter equation for quantum and classical 6j-symbols.

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