Anti-commutative Grobner-Shirshov basis of a free Lie algebra

被引：15

作者：

Bokut, L. A. ^{[1
,2
]}

Chen YuQun ^{[1
]}

Li Yu ^{[1
]}

机构：

[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[2] Russian Acad Sci, Sobolev Inst Math, Siberian Branch, Novosibirsk 630090, Russia

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2009年 / 52卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Lie algebra; anti-commutative algebra; Hall words; Grobner-Shirshov basis; SINGULARITIES; RESOLUTION; VARIETY; FIELD;

D O I：

10.1007/s11425-008-0168-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The concept of Hall words was first introduced by P. Hall in 1933 in his investigation on groups of prime power order. Then M. Hall in 1950 showed that the Hall words form a basis of a free Lie algebra by using direct construction, that is, first he started with a linear space spanned by Hall words, then defined the Lie product of Hall words and finally checked that the product yields the Lie identities. In this paper, we give a Grobner-Shirshov basis for a free Lie algebra. As an application, by using the Composition-Diamond lemma established by Shirshov in 1962 for free anti-commutative (non-associative) algebras, we provide another method different from that of M. Hall to construct a basis of a free Lie algebra.

引用

页码：244 / 253

页数：10

共 19 条

[11]

Magnus W, 1937, J REINE ANGEW MATH, V177, P105

[12]

Reutenauer C, 1993, LMS Monographs

[13]

Shirshov A. I., 1999, SIGSAM Bulletin, V33, P3, DOI 10.1145/334714.334715

[14]

Shirshov A.I., 1958, MAT SBORNIK, V45, P113

[15]

Shirshov A.I., 1962, Algebra Logika, V1, P14

[16]

Shirshov A.I., 1962, SIBIRSK MAT ZH, V3, P132

[17]

Shirshov A. I., 1954, Mat. Sb., V34, P81

[18]

Witt E, 1937, J REINE ANGEW MATH, V177, P152

[19]

[No title captured]

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