Journal article, 2016

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.5, the classical double D(sl(n, F), delta) is isomorphic to sl(n,F) circle times(F) A, where A is either F[epsilon], with epsilon(2) = 0, or F circle plus 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. For the Cremmer-Gervais r-matrix in sl(3), we also construct a natural map of sets between the total Belavin-Drinfeld twisted cohomology set and the Brauer group of the field F.

algebras

r-matrix

Brauer

Quadratic field

Classical double

Lie bialgebra

Admissible triple

Mathematics

Quantum group

Chalmers, Mathematical Sciences

University of Gothenburg

Chalmers, Mathematical Sciences

University of Gothenburg

0001-8708 (ISSN) 1090-2082 (eISSN)

Vol. 293 324-342Mathematics

10.1016/j.aim.2016.02.002