Nonstandard quantum groups associated to Belavin-Drinfeld triples

1996/09/23 by Timothy J. Hodges, Hodges, Timothy J.
Mathematics · #17B37 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B37 #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9609029

AMSLatex, 8 pages

arxiv created 1996/09/23 · openalex publication_date 1996/09/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A construction is given of a family of non-standard quantizations of the algebra of functions on a connected complex semi-simple algebraic group. For each ``disjoint'' triple in the sense of Belavin and Drinfeld, a 2-cocycle is constructed on certain multi-parameter quantum groups. The new non-standard quantum groups are the Hopf algebras obtained by twisting the known quantum groups by these 2-cocycles. In particular, the Cremmer-Gervais quantization of SL(3) can be constructed in this way.

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