Bicrossproduct Hopf quasigroups

2009/11/16 by J. Klim, Shahn Majid, Klim, J. +2
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Mathematics and Applications #Quantum Algebra (math.QA) #graph theory and CDMA systems #math.CO #math.GR #math.QA

paper · pdf · doi:10.48550/arxiv.0911.3114

16 pages latex no figures

arxiv created 2009/11/16 · openalex publication_date 2009/11/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We recall the notion of Hopf quasigroups introduced previously. We construct a bicrossproduct Hopf quasigroup kM\bicross k(G) from every group X with a finite subgroup G⊂ X and IP quasigroup transversal M⊂ X subject to certain conditions. We identify the octonions quasigroup G_O as transversal in an order 128 group X with subgroup Z₂³ and hence obtain a Hopf quasigroup kG_O\lcocross k(Z₂³) as a particular case of our construction.

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