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Factorizations of Hopf quasigroups
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In this paper, we introduce the notion of factorization in the Hopf quasigroup setting, and we prove that if $A$ and $H$ are Hopf quasigroups such that their antipodes are isomorphisms, a Hopf quasigroup $X$ admits a factorization as $X=AH$ iff $X$ is isomorphic to a double cross product $A\bowtie H$ as Hopf quasigroups.
University of Debrecen/ Debreceni Egyetem
Title: Factorizations of Hopf quasigroups
Description:
In this paper, we introduce the notion of factorization in the Hopf quasigroup setting, and we prove that if $A$ and $H$ are Hopf quasigroups such that their antipodes are isomorphisms, a Hopf quasigroup $X$ admits a factorization as $X=AH$ iff $X$ is isomorphic to a double cross product $A\bowtie H$ as Hopf quasigroups.
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