
Journal of Lie Theory 18 (2008), No. 1, 125140 Copyright Heldermann Verlag 2008 Braided Lie Bialgebras Associated to KacMoody Algebras Jan E. Grabowski Keble College, Oxford OX1 3PG, England jan.grabowski@maths.ox.ac.uk BraidedLie bialgebras have been introduced by Majid, as the Lie versions of Hopf algebras in braided categories. In this paper we extend previous work of Majid and of ours to show that there is a braidedLie bialgebra associated to each inclusion of KacMoody bialgebras. Doing so, we obtain many new examples of infinitedimensional braidedLie bialgebras. We analyze further the case of untwisted affine KacMoody bialgebras associated to finitedimensional simple Lie algebras. The inclusion we study is that of the finitetype algebra in the affine algebra. This braidedLie bialgebra is isomorphic to the current algebra over the simple Lie algebra, now equipped with a braided cobracket. We give explicit expressions for this braided cobracket for the simple Lie algebra sl_{3}. Keywords: KacMoody algebra, braided Lie bialgebra. MSC: 17B67, 17B62, 22E67 [ Fulltextpdf (216 KB)] for subscribers only. 