Weak Hopf algebras arising from weak matched pairs

2024/08/09 by Graziela Fonseca, Fonseca, Graziela, Grasiela Martini +3
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2408.05181

Abstract

This work extends the idea of matched pairs presented by Majid in \citeMajid and Takeuchi in \citeTakeuchi for the context of weak bialgebras and weak Hopf algebras. We introduce, also inspired by partial matched pairs \citematchedpair, 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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• A Duality Theorem for Weak Multiplier Hopf Algebra Actions
• Weak Partial Representations