A triple construction for Lie bialgebras

Details A triple construction for Lie bialgebras A triple construction for Lie bialgebras

2003-12-30

arxiv.org/abs/math/0312507v4

Pacific J. Math, 221, no. 2 (2005): 281-301

Mathematics

Quantum Algebra

24 pages. Changes: (v.2) reorganisation of Section 5, (v.3) introduction expanded and references added, (v.4) typos. Final ver

Scientific paper

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 $g \oplus g \oplus g$ by a certain cocycle. We also consider real forms of the triple and the triangular case.

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