Grobner-Shirshov Bases for Plactic Algebras

被引：9
|
作者：
Kubat, Lukasz [1 ]
Okninski, Jan [2 ]
机构：
[1] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland
[2] Warsaw Univ, Inst Math, PL-02097 Warsaw, Poland
来源：
ALGEBRA COLLOQUIUM | 2014年 / 21卷 / 04期
关键词：
plactic monoid; Grobner-Shirshov basis; semigroup algebra;
D O I：
10.1142/S1005386714000534
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A finite Grobner-Shirshov basis is constructed for the plactic algebra of rank 3 over a field K. It is also shown that plactic algebras of rank exceeding 3 do not have finite Grobner-Shirshov bases associated to the natural degree-lexicographic ordering on the corresponding free algebra. The latter is in contrast with the case of a strongly related class of algebras, called Chinese algebras.
引用
收藏
页码：591 / 596
页数：6
相关论文
共 50 条
  • [1] Finite Grobner-Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids
    Cain, Alan J.
    Gray, Robert D.
    Malheiro, Antonio
    JOURNAL OF ALGEBRA, 2015, 423 : 37 - 53
  • [2] Grobner-Shirshov bases for brace algebras
    Li, Yu
    Mo, Qiuhui
    Zhao, Xiangui
    COMMUNICATIONS IN ALGEBRA, 2018, 46 (11) : 4577 - 4589
  • [3] Grobner-Shirshov Bases for Extensions of Algebras
    Chen, Yuqun
    ALGEBRA COLLOQUIUM, 2009, 16 (02) : 283 - 292
  • [4] Grobner-Shirshov Bases for Replicated Algebras
    Kolesnikov, P. S.
    ALGEBRA COLLOQUIUM, 2017, 24 (04) : 563 - 576
  • [5] GROBNER-SHIRSHOV BASES AND EMBEDDINGS OF ALGEBRAS
    Bokut, L. A.
    Chen, Yuqun
    Mo, Qiuhui
    INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2010, 20 (07) : 875 - 900
  • [6] New approaches to plactic monoid via Grobner-Shirshov bases
    Bokut, L. A.
    Chen, Yuqun
    Chen, Weiping
    Li, Jing
    JOURNAL OF ALGEBRA, 2015, 423 : 301 - 317
  • [7] Grobner-Shirshov bases for metabelian Lie algebras
    Chen, Yongshan
    Chen, Yuqun
    JOURNAL OF ALGEBRA, 2012, 358 : 143 - 161
  • [8] Grobner-Shirshov bases for some Lie algebras
    Chen, Yu.
    Li, Y.
    Tang, Q.
    SIBERIAN MATHEMATICAL JOURNAL, 2017, 58 (01) : 176 - 182
  • [9] GROBNER-SHIRSHOV BASES FOR L-ALGEBRAS
    Bokut, L. A.
    Chen, Yuqun
    Huang, Jiapeng
    INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2013, 23 (03) : 547 - 571
  • [10] Grobner-Shirshov bases for quantum enveloping algebras
    Bokut, L
    Malcolmson, P
    ISRAEL JOURNAL OF MATHEMATICS, 1996, 96 : 97 - 113
12345