Characterization of Hopf Quasigroups
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 CH(α,β) with α,β∈ G over H and construct a new braided π-category C(H) with all the categories CH(α,β) as components.
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