On quantum groups and Lie bialgebras related to sl(n)

3Quantum: Algebra Geometry Information

物理学;数学

Stolin, A.^1 ; Pop, I.^1

Department of Mathematical Sciences, University of Gothenburg, Gothenburg

SE-405 30, Sweden^1

关键词: admissible triple;    Bialgebras;    classical double;    Quantum groups;    R matrices;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/532/1/012026/pdf
DOI  :  10.1088/1742-6596/532/1/012026

来源: IOP

【 摘 要 】

Given an arbitrary field F of characteristic 0, we study Lie bialgebra structures on sl(n; F), based on the description of the corresponding classical double. For any Lie bialgebra structure δ, the classical double D(sl(n; F);δ) is isomorphic to sl(n; F)FA, where A is either F[Ε], with Ε2= 0, or F × F or a quadratic field extension of F. In the first case, the classification leads to quasi-Frobenius Lie subalgebras of sl(n; F). In the second and third cases, a Belavin-Drinfeld cohomology can be introduced which enables one to classify Lie bialgebras on sl(n; F), up to gauge equivalence. The Belavin-Drinfeld untwisted and twisted cohomology sets associated to an r-matrix are computed.