Some remarks on the Akivis algebras and the Pre-Lie algebras

Title:

Some remarks on the Akivis algebras and the Pre-Lie algebras

Creator:

Chen, Yuqon and Li, Yu

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:be7167c2-a658-4d52-86c9-84a6ee52ec4d
uuid:be7167c2-a658-4d52-86c9-84a6ee52ec4d

Subject:

non-associative algebra, Akivis algebra, universal enveloping algebra, Pre-Lie algebra, and Gröbner-Shirshov basis

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper, by using the Composition-Diamond lemma for non-associative algebras invented by A. I. Shirshov in 1962, we give Gröbner-Shirshov bases for free Pre-Lie algebras and the universal enveloping non-associative algebra of an Akivis algebra, respectively. As applications, we show I. P. Shestakov's result that any Akivis algebra is linear and D. Segal's result that the set of all good words in $X^{**}$ forms a linear basis of the free Pre-Lie algebra ${\rm PLie}(X)$ generated by the set $X$. For completeness, we give the details of the proof of Shirshov's Composition-Diamond lemma for non-associative algebras.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

707-720

Source:

Czechoslovak Mathematical Journal | 2011 Volume:61 | Number:3

Harvested from:

CDK

Metadata only:

false