Quasiderivations and quasicentroids of Novikov algebras
type: Item
instance of: scholarly article
title: Quasiderivations and quasicentroids of Novikov algebras
zbMATH Open document ID: 1486.17002
author: Xin Zhou
author: Bing Sun
author: Liangyun Chen
author: Xiao-Dong Zhao
published in: Bulletin of the Iranian Mathematical Society
publication date: 2021-08-02T00:00:00Z
review text: A Novikov algebra is a nonassociative algebra satisfying the identities \(x(yz)-y(xz)=(xy-yx)z\) (left-symmetric algebra) and \((xy)z=(xz)y\). Given a nonassociative algebra \(A\), a linear endomorphism \(D\) of \(A\) is said to be a quasiderivation if there is a linear endomorphism \(D'\) such that \(D(x)y+xD(y)=D'(xy)\) for all \(x,y\in A\). \par The main result of the paper under review asserts that if \(A\) is a finite-dimensional Novikov algebra over a field of characteristic not two with \(A^2\neq 0\), such that any linear endomorphism of \(A\) is a quasiderivation, then the dimension of \(A\) is at most \(3\). Moreover, for any Novikov algebra \(A\), a nilpotent algebra \(B\), with \(B^3=0\), is constructed such that the Lie algebra of quasiderivations of \(A\) is naturally embedded in the Lie algebra of derivations of \(B\). The algebra \(B\) is the tensor product of \(A\) with the unique nontrivial nilpotent commutative associative algebra of dimension \(2\). Remark: Some of the results, and their proofs, are valid for arbitrary nonassociative algebras.
reviewed by: Alberto Elduque
Mathematics Subject Classification ID: 17A30
Mathematics Subject Classification ID: 17A36
zbMATH DE Number: 7377338
zbMATH Keywords: Novikov algebra
zbMATH Keywords: quasiderivation
zbMATH Keywords: generalized derivation
MaRDI profile type: Publication
full work available at URL: s41980-020-00416-3
OpenAlex ID: W3033788393
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DOI: 10.1007/S41980-020-00416-3
description: scientific article; zbMATH DE number 7377338