Duplication of algebras. IV
type: Item
instance of: scholarly article
title: Duplication of algebras. IV
zbMATH Open document ID: 1250.17041
author: Arie Hendrik Boers
published in: Indagationes Mathematicae. New Series
publication date: 2011-11-29T00:00:00Z
review text: This is posthume continuation of a series of papers by the author. Given a \(K\) algebra \(A\) we denote bt \(D_{K,nc}(A)\) the algebra structure defined on the \(K\)-vector space \(A\otimes A\) by the product \((x\otimes y)(x'\otimes y')=xy\otimes x'y'\). This is called the non-commutative duplicated of \(A\). If \(A\) is commutative, its duplicated is not commutative in general (the same holds for associativity). Nevertheless, if \(A\) is a finite dimensional associative algebra, its duplicated is 4-associative. This paper gives conditions in which the duplicated algebra of a given algebra \(A\) is flexible, Lie admissible or \(n\)-associative. At the end of the paper a short note wirtten by A. Micali, M. Ouattara and N. B. Pilabré explains how this paper was prepared after the death of Prof. Arie Hendrik Boers.
Mathematics Subject Classification ID: 17D92
Mathematics Subject Classification ID: 17D99
zbMATH DE Number: 5982443
zbMATH Keywords: duplication of algebras
zbMATH Keywords: \(n\)-associative ring
zbMATH Keywords: Jordan algebras
zbMATH Keywords: Lie-admissible algebra
zbMATH Keywords: nonassociative algebra
reviewed by: Antonio M. Oller Marcén
MaRDI profile type: Publication
full work available at URL: j.indag.2011.08.001
OpenAlex ID: W1979450237
DOI: 10.1016/J.INDAG.2011.08.001
description: scientific article; zbMATH DE number 5982443