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- Title
On Free Pre-Lie Algebras.
- Authors
Li, Yu; Mo, Qiuhui
- Abstract
In this paper, we find Hall-Shirshov type bases for free pre-Lie algebras. We show that Segal's basis of a free pre-Lie algebra is a type of these bases. We give a nonassociative Gröbner-Shirshov basis S for a free pre-Lie algebra such that Irr( S) is a monomial basis (called normal words) of a free pre-Lie algebra, where Irr( S) is the set of all nonassociative words, not containing maximal nonassociative words of polynomials from S. We establish the Composition-Diamond lemma for free pre-Lie algebras over the basis of normal words and the degree breadth lexicographic ordering.
- Subjects
LIE algebras; NONASSOCIATIVE algebras; NONASSOCIATIVE rings; ORDERED groups; LEXICOGRAPHY
- Publication
Algebra Colloquium, 2017, Vol 24, Issue 2, p267
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386717000153