Jordan bialgebras and their relation to Lie bialgebras

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1997 English Publisher:Springer Science and Business Media LLCJournal:Algebra and Logic, volume 36, pages 1-15 (issn: 0002-5232, eissn: 1573-8302,

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Authors: V. N. Zhelyabin;

doi: 10.1007/bf02671949

Jordan bialgebras and their relation to Lie bialgebras

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Abstract

We develop the notion of Jordan bialgebras and study the way in which such are related to Lie bialgebras. In particular, it is shown that if a Lie algebra L(J) obtained from a Jordan algebra J by applying the Kantor-Koecher-Tits construction admits the structure of a Lie bialgebra, under some natural constraints, then, J permits the structure of a Jordan algebra.

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