Mutation algebras of a nonassociative algebra
type: Item
instance of: scholarly article
title: Mutation algebras of a nonassociative algebra
zbMATH Open document ID: 0836.17002
DOI: 10.1016/0019-3577(95)98198-K
published in: Indagationes Mathematicae. New Series
publication date: 1996-05-02T00:00:00Z
review text: This paper contains some results on classes of Lie-admissible (nonassociative) algebras and their (left) \((p,q)\)-mutation algebras, defined by the altered product \(x \circ y : = (xp)y - (yq)x\). It is shown that every mutation of an assosymmetric algebra (defined by the property that the associator of any three elements is unchanged by permutations of these, yet not every associator is zero) is Lie-admissible. A weaker result is shown to hold for Vinberg algebras (also known as left-symmetric algebras): For every element \(r\) in the right nucleus of a Vinberg algebra, the \((r,r)\)-mutation is Lie-admissible.
Mathematics Subject Classification ID: 17A30
Mathematics Subject Classification ID: 17D25
zbMATH DE Number: 816058
zbMATH Keywords: Lie-admissible algebras
zbMATH Keywords: \((p,q)\)-mutation algebras
zbMATH Keywords: assosymmetric algebra
zbMATH Keywords: associator
zbMATH Keywords: Vinberg algebras
zbMATH Keywords: left-symmetric algebras
zbMATH Keywords: nucleus
author: Arie Hendrik Boers
reviewed by: S Walcher
MaRDI profile type: Publication
cites work: On assosymmetric rings
cites work: Q3346469
cites work: Q3712465
cites work: Q3712464
cites work: Q4037274
cites work: Q3043344
cites work: Q5570256
Recommended article: Q3981796
Recommended article: Q3712465
Recommended article: Q4316278
Recommended article: Q4299593
Recommended article: Q3138854
Recommended article: Identities in mutations of associative algebras*
Recommended article: Q3618729
Recommended article: Q4011594
Recommended article: Q3712464
Recommended article: Q4324528
description: scientific article; zbMATH DE number 816058