FREE BRACE ALGEBRAS ARE FREE PRE-LIE ALGEBRAS

被引：10

作者：

Foissy, Loic ^{[1
]}

机构：

[1] Univ Reims, Math Lab, FRE3111, F-51687 Reims 2, France

来源：

COMMUNICATIONS IN ALGEBRA | 2010年 / 38卷 / 09期

关键词：

Brace algebras; Pre-Lie algebras; HOPF-ALGEBRAS; ROOTED TREES; THEOREM;

D O I：

10.1080/00927870903115000

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let g be a free brace algebra. This structure implies that g is also a pre-Lie algebra and a Lie algebra. It is already known that g is a free Lie algebra. We prove here that g is also a free pre-Lie algebra, using a description of g with the help of planar rooted trees, a permutative product, and manipulations on the Poincare-Hilbert series of g.

引用

页码：3358 / 3369

页数：12

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