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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References
M. E. Sweedler,Hopf Algebras, Benjamin, New York (1969).
V. G. Drinfeld, “Hamiltonian structures on Lie groups, Lie bialgebras, and geometric meaning of the classical Yang-Baxter equations,”Dok. Akad. Nauk SSSR,268, No. 2, 285–287 (1983).
W. Michaelis, “Lie coalgebras,”Adv. Math.,38, 1–54 (1980).
A. Anquela, T. Cortes, and F. Montaner, “Nonassociative coalgebras,”Comm. Alg.,22, No. 12, 4693–4716 (1994).
V. N. Zhelyabin, “The Kantor-Koecher-Tits construction for Jordan coalgebras,”Algebra Logika,35, No. 2, 173–189 (1996).
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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.
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Zhelyabin, V.N. Jordan bialgebras and their relation to Lie bialgebras. Algebr Logic 36, 1–15 (1997). https://doi.org/10.1007/BF02671949
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DOI: https://doi.org/10.1007/BF02671949