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TitleAnti-commutative Gr\"obner-Shirshov basis of a free Lie algebra.
Author(s) Yuri A. Blinkov, Leonid A. Bokut, Yu-Fu Chen
TypeArticle in Journal
AbstractThe 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 Gröbner-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.
KeywordsLie algebra, anti-commutative algebra, Hall words, Gröbner-Shirshov basis
ISSN1006-9283; 1862-2763/e
URL http://link.springer.com/article/10.1007%2Fs11425-008-0168-y
JournalSci. China, Ser. A
PublisherScience in China Press, Beijing; Springer, Heidelberg
Translation No
Refereed No