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.
引用
收藏
页数：21
相关论文
共 64 条
  • [11] Grobner-Shirshov bases and their calculation
    Bokut, L. A.
    Chen, Yuqun
    [J]. BULLETIN OF MATHEMATICAL SCIENCES, 2014, 4 (03) : 325 - 395
  • [12] Bokut LA, 2012, PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON ALGEBRA 2010: ADVANCES IN ALGEBRAIC STRUCTURES, P53
  • [13] GROBNER-SHIRSHOV BASES FOR L-ALGEBRAS
    Bokut, L. A.
    Chen, Yuqun
    Huang, Jiapeng
    [J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2013, 23 (03) : 547 - 571
  • [14] GROBNER-SHIRSHOV BASES AND EMBEDDINGS OF ALGEBRAS
    Bokut, L. A.
    Chen, Yuqun
    Mo, Qiuhui
    [J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2010, 20 (07) : 875 - 900
  • [15] Grobner-Shirshov bases for associative algebras with multiple operators and free Rota-Baxter algebras
    Bokut, L. A.
    Chen, Yuqun
    Qiu, Jianjun
    [J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2010, 214 (01) : 89 - 100
  • [16] Bokut L.A., 1994, ALGORITHMIC COMBINAT
  • [17] Bokut L. A., 1976, Algebra Logika, V15, P117, DOI [10.1007/bf01877233, DOI 10.1007/BF01877233]
  • [18] Bokut L.A., 2000, FUNDAM APPL MATH, V6, P669
  • [19] Bokut L.A., 1972, IZV AKAD NAUK SSSR M, V36, P1173
  • [20] Bokut L.A., 2003, J. Math. Sci. (N.Y., V116, P2894
1234567