A characterization of weak Hopf (co)quasigroups

2015/06/25 by J. N. Alonso Álvarez, Álvarez, J. N. Alonso, J. M. Fernández Vilaboa +3
Mathematics · #16T05 #17A30 #18D10 #20N05 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1506.07664

openalex publication_date 2015/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show that weak Hopf (co)quasigroups can be characterized by a Galois-type condition. Taking into account that this notion generalizes the ones of Hopf (co)quasigroup and weak Hopf algebra, we obtain as a consequence the first fundamental theorem for Hopf (co)quasigroups and a characterization of weak Hopf algebras in terms of bijectivity of a Galois-type morphism (also called fusion morphism).

Related

• Weak Hopf Quasigroups
• Cleft and Galois extensions associated to a weak Hopf quasigroup
• Characterization of Hopf Quasigroups
• Hopf modules and the fundamental theorem for Hopf (co)quasigroups
• Braided crossed category over crossed group-cograded weak Hopf quasigroups