On Free Pre-Lie Algebras

• 来源期刊: 代数集刊（英文版）
• 关键词: nonassociative algebra pre-Lie algebra Gr(o)bner-Shirshov basis
• 年，卷（期）: 2017,（2）
• 页码范围: 267-284
• 页数: 18页
• 语种: 英文
• DOI: 10.1142/S1005386717000153

摘要

In this paper,we find Haal-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 Gr(o)bner-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.