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

Details Anti-commutative Groebner-Shirshov basis of a free Lie algebra Anti-commutative Groebner-Shirshov basis of a free Lie algebra

2008-04-06

arxiv.org/abs/0804.0914v1

Science in China, 52(2)(2009), 244-253.

Mathematics

Rings and Algebras

Scientific paper

One of the natural ways to prove that the Hall words (Philip Hall, 1933) consist of a basis of a free Lie algebra is a direct construction: to start with a linear space spanned by Hall words, to define the Lie product of Hall words, and then to check that the product yields the Lie identities (Marshall Hall, 1950). Here we suggest another way using the Composition-Diamond lemma for free anti-commutative (non-associative) algebras (A.I. Shirshov, 1962).

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