English

A triple construction for Lie bialgebras

Quantum Algebra 2007-05-23 v4

Abstract

We introduce and study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfeld double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the algebraic structure of the triple, analogous to known results for the double. Among them, we prove that in the factorisable case the triple is isomorphic to a twisting of gggg \oplus g \oplus g by a certain cocycle. We also consider real forms of the triple and the triangular case.

Keywords

Cite

@article{arxiv.math/0312507,
  title  = {A triple construction for Lie bialgebras},
  author = {Jan E. Grabowski},
  journal= {arXiv preprint arXiv:math/0312507},
  year   = {2007}
}

Comments

24 pages. Changes: (v.2) reorganisation of Section 5, (v.3) introduction expanded and references added, (v.4) typos. Final version, to appear Pacific J. Math