Grobner-Shirshov bases for Lie Ω-algebras and free Rota-Baxter Lie algebras

被引：6
作者：
Qiu, Jianjun [1 ]
Chen, Yuqun [1 ]
机构：
[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2017年 / 16卷 / 10期
关键词：
Grobner-Shirshov basis; Lyndon-Shirshov word; Lie Omega-algebra; Rota-Baxter Lie algebra; Nijenhuis Lie algebra; ASSOCIATIVE ALGEBRAS; DENDRIFORM ALGEBRAS; DIAMOND LEMMA; OPERATORS; RING;
D O I：
10.1142/S0219498817501900
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We generalize the Lyndon-Shirshov words to the Lyndon-Shirshov Omega-words on a set X and prove that the set of all the nonassociative Lyndon-Shirshov Omega-words forms a linear basis of the free Lie Omega-algebra on the set X. From this, we establish Grobner-Shirshov bases theory for Lie Omega-algebras. As applications, we give Grobner-Shirshov bases of a free lambda-Rota-Baxter Lie algebra, of a free modified lambda-Rota-Baxter Lie algebra, and of a free Nijenhuis Lie algebra and, then linear bases of these three algebras are obtained.
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页数：21
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