Details:
Title  Lyndon–Shirshov basis and anticommutative algebras  Author(s)  Yuri A. Blinkov, Leonid A. Bokut, YuFu Chen  Type  Article in Journal  Abstract  Chen, Fox, Lyndon (1958) [10] and Shirshov (1958) [29] introduced nonassociative Lyndon–Shirshov words and proved that they form a linear basis of a free Lie algebra, independently. In this paper we give another approach to definition of Lyndon–Shirshov basis, i.e., we find an anticommutative Gröbner–Shirshov basis S of a free Lie algebra such that Irr ( S ) is the set of all nonassociative Lyndon–Shirshov words, where Irr ( S ) is the set of all monomials of N ( X ) , a basis of the free anticommutative algebra on X, not containing maximal monomials of polynomials from S. Following from Shirshovʼs anticommutative Gröbner–Shirshov bases theory (Shirshov, 1962 [32]), the set Irr ( S ) is a linear basis of a free Lie algebra.  Keywords  Lie algebra, Anticommutative algebra, Lyndon–Shirshov words, Gröbner–Shirshov basis  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869313000057 
Language  English  Journal  Journal of Algebra  Volume  378  Pages  173  183  Year  2013  Edition  0  Translation 
No  Refereed 
No 
