结合超代数上的超结合Yang-Baxter方程  

Super associative Yang-Baxter equation in associative superalgebras

作　　者：安慧辉[1] AN Huihui(School of Mathematics,Liaoning Normal University,Dalian 116029,China)

机构地区：[1]辽宁师范大学数学学院

出　　处：《辽宁师范大学学报（自然科学版）》2019年第2期152-157,共6页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：主要研究结合超代数上的超结合Yang-Baxter方程.首先给出结合超代数上Rota-Baxter算子和■-算子的定义,得到结合超代数上奇的Rota-Baxter算子与李超代数上奇的Rota-Baxter算子之间的关系,找到结合超代数上的超结合Yang-Baxter方程的解与结合超代数上的■-算子之间的关系.最后给出了结合超代数上超结合YangBaxter方程的解与超2-上循环之间的关系.In this paper we study the super associative Yang-Baxter equation in associative superalgebras.First we give the definition of Rota-Baxter operator and ■-operator in associative superalgebra.We also give the relation between the odd Rota-Baxter operator in associative superalgebra and Lie superalgebra.Then we give the relation between the solution of super associative Yang-Baxter equation and ■-operator in associative superalgebra.At last,we give the relation between the solution of super associative Yang-Baxter equation and super 2-cocycle in associative superalgebra.

关 键 词：超结合Yang-Baxter方程 ■-算子 2-上循环 

分 类 号：O152.5[理学—数学]