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A triple construction for Lie bialgebras

Research output: Contribution to journalJournal article

Published

Journal publication date2005
JournalPacific Journal of Mathematics
Journal number2
Volume221
Number of pages22
Pages281-301
Original languageEnglish

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.