科研之友
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摘要
Chen, Fox, Lyndon (1958) [10] and Shirshov (1958) [29] introduced non-associative 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 anti-commutative Grobner-Shirshov basis S of a free Lie algebra such that Irr(S) is the set of all non-associative Lyndon-Shirshov words, where Irr(S) is the set of all monomials of N(X), a basis of the free anti-commutative algebra on X, not containing maximal monomials of polynomials from S. Following from Shirshov's anti-commutative Grobner-Shirshov bases theory (Shirshov, 1962 [32]), the set Irr(S) is a linear basis of a free Lie algebra.
- 出版日期2013-3-15
- 单位华南师范大学
