L-quadri代数  

L-quadri-algebras

作　　者：刘立功[1,2] 倪翔[1,2] 白承铭[1,2] 

机构地区：[1]南开大学陈省身数学研究所,天津300071 [2]核心数学与组合数学教育部重点实验室,天津300071

出　　处：《中国科学：数学》2011年第2期105-124,共20页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:10621101;10921061);国家重点基础研究发展计划(批准号:2006CB805905);教育部博士点基金(批准号:200800550015)资助项目

摘　　要：Quadri代数是由Aguiar和Loday引入的一类著名的Loday代数.在本文中,我们引入具有4个运算的L-quadri代数的概念,它满足广义左对称性,其4个运算的和的换位运算是Lie代数,并且是quadri代数的Lie代数类似结构.任何quadri代数是L-quadri代数,并且L-quadri代数可以放在Loday代数与它们的Lie代数类似结构之间关系(即推广结合代数的换位运算是Lie代数的著名事实)的框架下.我们也给出了L-quadri代数与诸如Rota-Baxter算子、经典Yang-Baxter方程和满足某些条件的双线性型等一些有意义结构之间的密切关系.Quadri-algebras introduced by Aguiar and Loday are a class of remarkable Loday algebras. In this paper, we introduce a notion of L-quadri-algebra with 4 operations satisfying certain generalized left-symmetry, as a Lie algebraic analogue of quadri-algebra such that the commutator of the sum of the 4 operations is a Lie algebra. Any quadri-algebra is an L-quadri-algebra. Moreover, L-quadri-algebras fit into the framework of the relationships between Loday algebras and their Lie algebraic analogues, extending the well known fact that the commutator of an associative algebra is a Lie algebra. We also give the close relationships between L-quadri- algebras and some interesting structures like Rota-Baxter operators, classical Yang-Baxter equation and some bilinear forms satisfying certain conditions.

关 键 词：LIE代数 Loday代数 quadri代数 经典Yang-Baxter方程 O-算子 

分 类 号：O153[理学—数学]