Construction of quasi-linear left cycle sets

被引：6

作者：

Catino, Francesco ^{[1
]}

Miccoli, Maria Maddalena ^{[1
]}

机构：

[1] Univ Salento, Dipartimento Matemat & Fis E De Giorgi, I-73100 Lecce, Italy

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2015年 / 14卷 / 01期

关键词：

Quantum Yang-Baxter equation; set-theoretic solution; cycle set; THEORETICAL SOLUTIONS; BAXTER;

D O I：

10.1142/S0219498815500012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we produce a method to construct quasi-linear left cycle sets A with Rad(A) subset of Fix(A). Moreover, among these cycle sets, we give a complete description of those for which Fix(A) = Soc(A) and the underlying additive group is cyclic. Using such cycle sets, we obtain left non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation which are different from those obtained in [P. Etingof, T. Schedler and A. Soloviev, Set-theoretical solutions to the quantum Yang-Baxter equation, Duke Math. J. 100 (1999) 169-209; P. Etingof, A. Soloviev and R. Guralnick, Indecomposable set-theoretical solutions to the quantum Yang-Baxter equation on a set with a prime number of elements, J. Algebra 242 (2001) 709-719].

引用

页数：7

共 15 条

[1]

[Anonymous], 2007, Colloq. Math.

[2] REGULAR SUBGROUPS OF THE AFFINE GROUP AND RADICAL CIRCLE ALGEBRAS [J].