弱 Hopf 拟群与拟广群体的匹配对
Weak Hopf quasigroups and matched pairs of quasigroupoids
AI总结：
本文提出拟广群体的精确分解与匹配对概念，证明匹配对可构造双重交叉积，并揭示其与弱 Hopf 拟群的关联。
摘要：
本文引入了拟广群体（quasigroupoid）的精确分解概念以及具有共同基的拟广群体匹配对的概念。我们证明了如果 $({\sf A}, {\sf H})$ 是拟广群体的一个匹配对，则可以构造一个新的拟广群体 ${\sf A}\bowtie {\sf H}$，称为 ${\sf A}$ 和 ${\sf H}$ 的双重交叉积。此外，我们证明了如果一个拟广群体 ${\sf B}$ 允许精确分解，则存在一个拟广群体匹配对 $({\sf A}, {\sf H})$ 以及 ${\sf A}\bowtie {\sf H}$ 与 ${\sf B}$ 之间的拟广群体同构。最后，如果 ${\mathbb K}$ 是一个域，我们证明了每个拟广群体匹配对 $({\sf A}, {\sf H})$ 通过拟广群体 magma 构造，诱导出一对 $({\mathbb K}[{\sf A}], {\mathbb K}[{\sf H}])$ 的弱 Hopf 拟群，以及一个双重交叉积弱 Hopf 拟群 ${\mathbb K}[{\sf A}]\bowtie{\mathbb K}[{\sf H}]$，它与 ${\mathbb K}[{\sf A}\bowtie {\sf H}]$ 作为弱 Hopf 拟群同构。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
