A triple construction for Lie bialgebras

Jan E. Grabowski

Vol. 221 (2005), No. 2, 281–301

DOI: 10.2140/pjm.2005.221.281

Abstract

We study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfel’d double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the triple’s algebraic structure, analogous to known results for the Drinfel’d double: among them, that in the factorisable case the triple is isomorphic to a twisting of g ⊕ g ⊕ g by a certain cocycle. We also consider real forms of the triple and the triangular case.

Keywords

triple, Lie bialgebra, Drinfel’d double

Mathematical Subject Classification 2000

Primary: 17B62

Milestones

Received: 14 January 2004

Revised: 1 June 2004

Accepted: 3 December 2004

Published: 1 October 2005