2024/03/14 by R. González Rodrı́guez, Rodríguez, Ramón González
Business, Management and Accounting · Engineering · Mathematics · #16T05 #17A01 #20N05 #FOS: Mathematics #Mathematics and Applications #Optics and Image Analysis #Rings and Algebras (math.RA) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2403.09231
openalex publication_date 2024/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce the notion of exact factorization of a quasigroupoid and the notion of matched pair of quasigroupoids with common base. We prove that if (\sf A, \sf H) is a matched pair of quasigroupoids it is posible to construct a new quasigroupoid \sf A\bowtie \sf H called the double cross product of \sf A and \sf H. Also, we show that, if a quasigroupoid \sf B admits an exact factorization, there exists a matched pair of quasigroupoids (\sf A, \sf H) and an isomorphism of quasigroupoids between \sf A\bowtie \sf H and \sf B. Finally, if \mathbb K is a field, we show that every matched pair of quasigroupoids (\sf A, \sf H) induce, thanks to the quasigroupoid magma construction, a pair (\mathbb K[\sf A], \mathbb K[\sf H]) of weak Hopf quasigroups and a double crossed product weak Hopf quasigroup \mathbb K[\sf A]\bowtie\mathbb K[\sf H] isomorphic to \mathbb K[\sf A\bowtie \sf H] as weak Hopf quasigroups.