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Siberian Mathematical Journal

, Volume 47, Issue 4, pp 767–778 | Cite as

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

  • Liang-yun Zhang
Article

Abstract

Given an (H,R)-Lie coalgebra Γ, we construct (H,R T )-Lie coalgebra ΓT 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, [, ], Δ, R) is an (H,R)-Lie bialgebra of an ordinary Lie algebra then (L T , [, ], ΔT, 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 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Liang-yun Zhang
    • 1
  1. 1.Nanjing Agricultural University; Nanjing UniversityNanjingP. R. China

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