On quantization of r-matrices for Belavin-Drinfeld Triples
نویسنده
چکیده
We suggest a formula for quantum universal R-matrices corresponding to quasitriangular classical r-matrices classified by Belavin and Drinfeld for all simple Lie algebras. The R-matrices are obtained by twisting the standard universal R-matrix.
منابع مشابه
Proof of the Ggs Conjecture
We prove the GGS conjecture [GGS] (1993), which gives a particularly simple explicit quantization of classical r-matrices for Lie algebras gl(n), in terms of a matrix R ∈ Matn(C) ⊗ Matn(C) which satisfies the quantum YangBaxter equation (QYBE) and the Hecke condition, whose quasiclassical limit is r. The r-matrices were classified by Belavin and Drinfeld in the 1980’s in terms of combinatorial ...
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1.1. Classical r-matrices. In the early eighties, Belavin and Drinfeld [BD] classified nonskewsymmetric classical r-matrices for simple Lie algebras. It turned out that such r-matrices, up to isomorphism and twisting by elements from the exterior square of the Cartan subalgebra, are classified by combinatorial objects which are now called Belavin-Drinfeld triples. By definition, a Belavin-Drinf...
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