Near braces and p$p$‐deformed braided groups
Near braces and p$p$‐deformed braided groups
复制标题
近支架和 p$p$变形编织组
DOI：
10.1112/blms.12918
复制
发表时间：
2023
影响因子：
0.9
通讯作者：
Bernard Rybołowicz
中科院分区：
文献类型：
--
作者：
A. Doikou;Bernard Rybołowicz
受最近关于杨-巴克斯特方程参数非对合解的推导结果的启发，我们重构了基本的代数结构，称为近花括号。利用近花括号的概念，我们得到了集合论Yang-Baxter方程的新的多参数、非退化、非对合解。这些解是由大括号和斜大括号得到的已知解的推广。还构造了与逆解相关的双射映射。进一步，我们引入了-变形辫子群和-辫子的广义概念，并证明了每个辫子都是辫子方程的解。我们还证明了在近支撑内的某些多参数映射提供了-辫子的特殊情况。
Motivated by recent findings on the derivation of parametric noninvolutive solutions of the Yang–Baxter equation, we reconstruct the underlying algebraic structures, called near braces. Using the notion of the near braces we produce new multi‐parametric, nondegenerate, noninvolutive solutions of the set‐theoretic Yang–Baxter equation. These solutions are generalizations of the known ones coming from braces and skew braces. Bijective maps associated to the inverse solutions are also constructed. Furthermore, we introduce the generalized notion of ‐deformed braided groups and ‐braidings and we show that every ‐braiding is a solution of the braid equation. We also show that certain multi‐parametric maps within the near braces provide special cases of ‐braidings.
从预制桁架到斜撑
DOI：
10.5565/publmat6622206
发表时间：
2022
期刊：
Publicacions Matemàtiques
影响因子：
--
作者：
Brzezinski T
通讯作者：
Brzezinski T
DOI：
10.48550/arxiv.1912.03091
发表时间：
2019
期刊：
--
影响因子：
--
作者：
Doikou A
通讯作者：
Doikou A