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Matched pairs of generalized Lie algebras and cocycle twists. (English) Zbl 1230.17015

Summary: We introduce the conception of matched pairs of \((H, \beta )\)-Lie algebras, and construct an \((H, \beta )\)-Lie algebra through them. We prove that the cocycle twist of a matched pair of \((H, \beta )\)-Lie algebras can also be matched.

MSC:

17B62 Lie bialgebras; Lie coalgebras
18D35 Structured objects in a category (MSC2010)
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