Fundamental theorems of Doi-Hopf modules in a nonassociative setting

2017/03/09 by J. N. Alonso Álvarez, Álvarez, J. N. Alonso, J. M. Fernández Vilaboa +3
Mathematics · Physics and Astronomy · #16T05 #17A30 #18D10 #20N05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1703.03229

openalex publication_date 2017/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce the notion of weak non-asssociative Doi-Hopf module and give the Fundamental Theorem of Hopf modules in this setting. Also we prove that there exists a categorical equivalence that admits as particular instances the ones constructed in the literature for Hopf algebras, weak Hopf algebras, Hopf quasigroups, and weak Hopf quasigroups.

Related

• Weak Hopf Quasigroups
• Hopf modules and the fundamental theorem for Hopf (co)quasigroups
• A characterization of weak Hopf (co)quasigroups
• Strong Hopf modules for weak Hopf quasigroups
• Doi-Hopf modules and Yetter-Drinfeld modules for quasi-Hopf algebras