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A triple construction for Lie bialgebras

Research output: Contribution to journalJournal article


<mark>Journal publication date</mark>2005
<mark>Journal</mark>Pacific Journal of Mathematics
Issue number2
Number of pages22
Pages (from-to)281-301
<mark>Original language</mark>English


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.