论文标题
对称偏斜的支架和支架系统
Symmetric skew braces and brace systems
论文作者
论文摘要
对于偏斜的左撑杆（g，\ cdot，\ circ）$，地图$λ：（g，circ）同态。然后，$λ$也可以看作是$（g，\ cdot）$到$ \ aut \，（g，\ cdot）$的地图，通常，这可能不是同构。如果$λ$ -Mormorphic（$λ$ -Homorphic）如果$λ：（g，\ cdot）\ to \ aut \，（g，\ cdot）$是一种反塑性（同构），则称为$λ$ -Ini-anti-homomorphic（$λ$ -HOMORPHIC）。我们主要研究这种偏斜的左括号。我们设备了一种在给定集合上构造一类二进制操作的方法，以便具有任何两个这样的操作的集合构成$λ$ - 巨型形状的对称偏斜支架。对称偏斜括号的大多数结构都在文献中处理在我们建筑的框架上。然后，我们对特定的无限集进行了各种此类结构。
For a skew left brace $(G, \cdot, \circ)$, the map $λ: (G, \circ) \to \Aut \,(G, \cdot),~~a \mapsto λ_a,$ where $λ_a(b) = a^{-1} \cdot (a \circ b)$ for all $a, b \in G$, is a group homomorphism. Then $λ$ can also be viewed as a map from $(G, \cdot)$ to $\Aut \, (G, \cdot)$, which, in general, may not be a homomorphism. A skew left brace will be called $λ$-anti-homomorphic ($λ$-homomorphic) if $λ: (G, \cdot) \to \Aut \, (G, \cdot)$ is an anti-homomorphism (a homomorphism). We mainly study such skew left braces. We device a method for constructing a class of binary operations on a given set so that the set with any two such operations constitute a $λ$-homomorphic symmetric skew brace. Most of the constructions of symmetric skew braces dealt with in the literature fall in the framework of our construction. We then carry out various such constructions on specific infinite sets.
