Weak Hopf algebras arising from weak matched pairs

Graziela Fonseca; Grasiela Martini; Leonardo Silva

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arXiv · 2408.05181

Weak Hopf algebras arising from weak matched pairs

Graziela Fonseca·Grasiela Martini·Leonardo Silva

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Abstract

This work extends the idea of matched pairs presented by Majid in \cite{Majid} and Takeuchi in \cite{Takeuchi} for the context of weak bialgebras and weak Hopf algebras. We introduce, also inspired by partial matched pairs \cite{matchedpair}, the notion of weak matched pairs and establish conditions for a subspace of the smash product be a weak bialgebra/Hopf algebra. Further, some new examples of (co)actions of weak bialgebras over algebras and some results about integral elements are presented.

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Graziela Fonseca, Grasiela Martini, Leonardo Silva. 2024-08-09. Weak Hopf algebras arising from weak matched pairs. https://arxiv.org/abs/2408.05181

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