Details:
Title  Anticommutative Gr\"obnerShirshov basis of a free Lie algebra.  Author(s)  Yuri A. Blinkov, Leonid A. Bokut, YuFu Chen  Type  Article in Journal  Abstract  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 GröbnerShirshov basis for a free Lie algebra. As an application, by using the CompositionDiamond lemma established by Shirshov in 1962 for free anticommutative (nonassociative) algebras, we provide another method different from that of M. Hall to construct a basis of a free Lie algebra.  Keywords  Lie algebra, anticommutative algebra, Hall words, GröbnerShirshov basis  ISSN  10069283; 18622763/e 
URL 
http://link.springer.com/article/10.1007%2Fs114250080168y 
Language  English  Journal  Sci. China, Ser. A  Volume  52  Number  2  Pages  244253  Publisher  Science in China Press, Beijing; Springer, Heidelberg  Year  2009  Edition  0  Translation 
No  Refereed 
No 
