Given an (H,R)-Lie coalgebra Γ, we construct (H,RT)-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 (LT, [, ], ΔT, RT) is an (H,RT)-Lie bialgebra of an ordinary Lie algebra.
(H,R)-Lie coalgebra triangular Hopf algebra right cocycle (H,R)-Lie bialgebra
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