This article is cited in 6 papers

Dual coalgebras of Jordan bialgebras and superalgebras

V. N. Zhelyabin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: 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.

Keywords: Hopf algebra, Lie bialgebra, Jordan bialgebra, Jordan superalgebra, nonassociative coalgebra, local finite dimensionality, dual coalgebra.

UDC: 512.554

Received: 26.05.2004

 English version: Siberian Mathematical Journal, 2005, 46:6, 1050–1061

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