Jordan bialgebras and their relation to Lie bialgebras

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. Supported by RFFR grant No. 95-01-01356 and by ISF grant No. RB 6300. Translated fromAlgebra i Logika, Vol. 36, No. 1, pp. 3–25, January–February, 1997.