Braces, radical rings, and the quantum Yang–Baxter equation
Braces, radical rings, and the quantum Yang–Baxter equation
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DOI：
10.1016/j.jalgebra.2006.03.040
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发表时间：
2007
影响因子：
0.9
通讯作者：
W. Rump
中科院分区：
文献类型：
--
作者：
W. Rump
非简并循环集等价于量子杨-巴克斯特方程的非简并酉集合论解。我们将这样的循环集嵌入到广义的根环（大括号）中，并在这种情况下研究它们的相互作用。我们在括号理想和商循环集之间建立了伽罗瓦理论。我们的主要结果确定了两个相互传递操作的无平方循环集之间的关系。
Non-degenerate cycle sets are equivalent to non-degenerate unitary set-theoretical solutions of the quantum Yang–Baxter equation. We embed such cycle sets into generalized radical rings (braces) and study their interaction in this context. We establish a Galois theory between ideals of braces and quotient cycle sets. Our main result determines the relationship between two square-free cycle sets operating transitively on each other.