Solutions of associative Yang-Baxter equation and D-equation in low dimensions and associated Frobenius algebras and Connes cocycles

被引：1
作者：
Hounkonnou, Mahouton Norbert [1 ]
Houndedji, Gbevewou Damien [1 ]
机构：
[1] Univ Abomey Calavi, ICMPA, UNESCO Chair, 072 BP 50, Cotonou, Littoral, Benin
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2018年 / 17卷 / 01期
关键词：
Associative algebra; Frobenius algebra; Connes cocycle; dendriform algebra; D-equation; Yang-Baxter equation; HOPF-ALGEBRAS; BIALGEBRAS; HOMOLOGY;
D O I：
10.1142/S021949881850010X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we compute solutions of the Yang-Baxter associative equation in dimensions one and two. For these solutions, we describe the double constructions of the associated Frobenius algebras, following Bai's definitions. Besides, we determine related compatible dendriform algebras and solutions of their D-equations. Finally, using symmetric solutions of these equations, we build the double constructions of related Connes cocycles.
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页数：26
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