This article is cited in 2 papers

$(H,R)$-Lie coalgebras and $(H,R)$-Lie bialgebras

L.-yu. Zhang

Agricultural University of Nanjing

Abstract: Given an $(H,R)$-Lie coalgebra $\Gamma$, we construct $(H,R_T)$-Lie coalgebra $\Gamma^T$ through a right cocycle $T$, where $(H,R)$ is a triangular Hopf algebra, and prove that there exists a bijection between the set of $(H,R)$-Lie coalgebras and the set of ordinary Lie coalgebras. We also show that if $(L,[,],\Delta,R)$ is an $(H,R)$-Lie bialgebra of an ordinary Lie algebra then $(L^T,[,],\Delta_T,R_T)$ is an $(H,R_T)$-Lie bialgebra of an ordinary Lie algebra.

Keywords: $(H,R)$-Lie coalgebra, triangular Hopf algebra, right cocycle, $(H,R)$-Lie bialgebra.

UDC: 512.554

Received: 21.03.2005

 English version: Siberian Mathematical Journal, 2006, 47:4, 767–778

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