Grobner-Shirshov Bases for Replicated Algebras

被引：5
|
作者：
Kolesnikov, P. S. [1 ]
机构：
[1] Sobolev Inst Math, Akad Koptyug Prosp 4, Novosibirsk 630090, Russia
来源：
ALGEBRA COLLOQUIUM | 2017年 / 24卷 / 04期
关键词：
di-algebra; tri-algebra; Grobner-Shirshov basis; LEIBNIZ ALGEBRAS; DIAMOND LEMMA; DIALGEBRAS;
D O I：
10.1142/S1005386717000372
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish a universal approach to solutions of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows us to apply Grobner-Shirshov bases method for Lie algebras to solve the ideal membership problem in free Leibniz algebras (Lie di-algebras). As another application, we prove an analogue of the Poincare-Birkhoff-Witt Theorem for universal enveloping associative tri-algebra of a Lie tri-algebra (CTD!-algebra).
引用
收藏
页码：563 / 576
页数：14
相关论文
共 50 条
  • [41] Defining relations and Grobner-Shirshov bases of Poisson algebras as of conformal modules
    Kolesnikov, P. S.
    Panasenko, A. S.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2022, 21 (07)
  • [42] Grobner-Shirshov bases for Lie Ω-algebras and free Rota-Baxter Lie algebras
    Qiu, Jianjun
    Chen, Yuqun
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2017, 16 (10)
  • [43] The graph based on Grobner-Shirshov bases of groups
    Karpuz, Eylem G.
    Ates, Firat
    Cevik, A. Sinan
    Cangul, I. Naci
    FIXED POINT THEORY AND APPLICATIONS, 2013,
  • [44] Grobner-Shirshov Bases for Exceptional Lie Superalgebras
    Lee, Dong-il
    ALGEBRA COLLOQUIUM, 2015, 22 (01) : 1 - 10
  • [45] INTERNET SECURITY APPLICATIONS OF GROBNER-SHIRSHOV BASES
    Kelarev, Andrei
    Yearwood, John
    Watters, Paul
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2010, 3 (03) : 435 - 442
  • [46] Comparing Grobner-Shirshov Bases and Word Reversing
    Autord, Marc
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2009, 33 (04) : 639 - 663
  • [47] Grobner-Shirshov Bases for Free Idempotent Monoids
    Ul Zaman, Baddi
    Chen, Yuqun
    Yang, Mingmei
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2021, 45 (05) : 759 - 774
  • [48] Grobner-Shirshov Basis for the Onsager and Tetrahedron Algebras
    Poroshenko, Evgeny
    COMMUNICATIONS IN ALGEBRA, 2013, 41 (02) : 435 - 450
  • [49] Grobner-Shirshov Bases for Temperley-Lieb Algebras of Complex Reflection Groups
    Lee, Jeong-Yup
    Lee, Dong-il
    Kim, SungSoon
    SYMMETRY-BASEL, 2018, 10 (10):
  • [50] Free Lie differential Rota-Baxter algebras and Grobner-Shirshov bases
    Qiu, Jianjun
    Chen, Yuqun
    INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2017, 27 (08) : 1041 - 1060
12345