论文标题
杨巴克斯特方程和扭曲的群体部门的基本解决方案
Idempotent solutions of the Yang-Baxter equation and twisted group division
论文作者
论文摘要
Yang-baxter方程的左左左溶液与扭曲的病房左式准群的对应关系，它们是满足身份$（x*y）*（x*z）*（x*z）=（y*y）=（y*y）*（y*z）$的左准群。使用Cayley内核的组合特性和平方映射，我们证明了扭曲的病房左序质量序列是排列或准元素。为了同构，所有扭曲的病房准流型$（x，*）$都是通过分组扭曲左部操作（即它们的形式为$ x*y =ψ（x^{ - 1} y）$的形式，用于$（x，x，\ cdot）$及其自动形状$ $ψ$及其对应的latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin latin solutian cootempottent latin latin latin latin latin latin latin。我们解决了基于拉丁语解决方案的同构问题。
Idempotent left nondegenerate solutions of the Yang-Baxter equation are in one-to-one correspondence with twisted Ward left quasigroups, which are left quasigroups satisfying the identity $(x*y)*(x*z)=(y*y)*(y*z)$. Using combinatorial properties of the Cayley kernel and the squaring mapping, we prove that a twisted Ward left quasigroup of prime order is either permutational or a quasigroup. Up to isomorphism, all twisted Ward quasigroups $(X,*)$ are obtained by twisting the left division operation in groups (that is, they are of the form $x*y=ψ(x^{-1}y)$ for a group $(X,\cdot)$ and its automorphism $ψ$), and they correspond to idempotent latin solutions. We solve the isomorphism problem for idempotent latin solutions.
