Exchange Dynamical Quantum Groups

1998/01/31 by Pavel Etingof, Alexander Varchenko · 6 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA

paper · pdf · doi:10.1007/s002200050665

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

arxiv created 1999/02/06 · openalex publication_date 1999/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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