Abstract
In this paper, extending the idea presented by Takeuchi in [M. Takeuchi, Matched pairs of groups and bismash products of Hopf algebras, Comm. Algebra 9 (1981) 841–882.] and more generally by Majid in [S. Majid, Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction, J. Algebra 130(1) (1990) 17–64.], we introduce the notion of partial matched pair [Formula: see text] involving the concepts of partial action and partial coaction between two bialgebras [Formula: see text] and [Formula: see text]. Furthermore, we present sufficient conditions for the corresponding bismash product [Formula: see text] to generate a new Hopf algebra and, as illustration, a family of examples is provided. Moreover, under some hypotheses such sufficient conditions are also necessary conditions.
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