Characterization of Hopf Quasigroups

2019/02/26 by Wei Wang, Wang, Wei, Shuanhong Wang +1 · 1 citation
Engineering · Mathematics · #16T05 #FOS: Mathematics #Mathematics and Applications #Quantum Algebra (math.QA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1902.10141

openalex publication_date 2019/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first discuss some properties of the Galois linear maps. We provide some equivalent conditions for Hopf algebras and Hopf (co)quasigroups as its applications. Then let H be a Hopf quasigroup with bijective antipode and G be the set of all Hopf quasigroup automorphisms of H. We introduce a new category \mathscrC_H(α,β) with α,β∈ G over H and construct a new braided π-category \mathscrC(H) with all the categories \mathscrC_H(α,β) as components.

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