On quantum groups and Lie bialgebras related to sl(n)
Paper in proceedings, 2014

Given an arbitrary field of characteristic 0, we study Lie bialgebra structures on sl(n, ), 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.

Lie bialgebra

quantum group

Author

Alexander Stolin

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Iulia Pop

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Journal of Physics Conference Series

Vol. 532 artikel nr 012026-

Subject Categories

Mathematics

Physical Sciences

DOI

10.1088/1742-6596/532/1/012026

More information

Created

10/7/2017