Exchange dynamical quantum groups

Abstract

For any simple Lie algebra g and any complex number q which is not zero or a nontrivial root of unity, we construct a dynamical quantum group (Hopf algebroid), whose representation theory is essentially the same as the representation theory of the quantum group U_q(g). This dynamical quantum group is obtained from the fusion and exchange relations between intertwining operators in representation theory of U_q(g), and is an algebraic structure standing behind these relations.

30 pages, latex; two short sections and some remarks were added

References in corpus (2)

• Geometry and classification of solutions of the Classical Dynamical Yang-Baxter Equation
• Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups

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