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Dual coalgebras of Jordan bialgebras and superalgebras. (Russian, English) Zbl 1118.17009
Sib. Mat. Zh. 46, No. 6, 1302-1315 (2005); translation in Sib. Math. J. 46, No. 6, 1050-1061 (2005).
Summary: W. Michaelis showed for Lie bialgebras that the dual coalgebra of a Lie algebra is a Lie bialgebra. In the present article we study an analogous question in the case of Jordan bialgebras. We prove that a simple infinite-dimensional Jordan superalgebra of vector type possesses a nonzero dual coalgebra. Thereby, we demonstrate that the hypothesis formulated by W. Michaelis for Lie coalgebras fails in the case of Jordan supercoalgebras.

MSC:
17C70 Super structures
16T15 Coalgebras and comodules; corings
16T10 Bialgebras
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