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Braided Lie bialgebras associated to Kac-Moody algebras

Grabowski, Jan (2008) Braided Lie bialgebras associated to Kac-Moody algebras. Journal of Lie Theory, 18 (1). pp. 125-140. ISSN 0949-5932

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    Abstract

    Braided-Lie 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 braided-Lie bialgebra associated to each inclusion of Kac-Moody bialgebras. Doing so, we obtain many new examples of infinite-dimensional braided-Lie bialgebras. We analyze further the case of untwisted affine Kac-Moody bialgebras associated to finite-dimensional simple Lie algebras. The inclusion we study is that of the finite-type algebra in the affine algebra. This braided-Lie 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 sl3.

    Item Type: Article
    Journal or Publication Title: Journal of Lie Theory
    Uncontrolled Keywords: Kac-Moody algebra, braided Lie bialgebra.
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 50167
    Deposited By: ep_importer_pure
    Deposited On: 28 Sep 2011 11:25
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 12:43
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/50167

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