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\((H,R)\)-Lie coalgebras and \((H,R)\)-Lie bialgebras. (Russian, English) Zbl 1135.17302
Sib. Mat. Zh. 47, No. 4, 932-945 (2006); translation in Sib. Math. J. 47, No. 4, 767-778 (2006).
Summary: 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 \((L,[\,,\,],\Delta_T,R)\) 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.
MSC:
17B62 Lie bialgebras; Lie coalgebras
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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