\((n+1)\)-ary derivations of simple \(n\)-ary algebras
type: Item
instance of: scholarly article
title: \((n+1)\)-ary derivations of simple \(n\)-ary algebras
zbMATH Open document ID: 1261.17002
author: I. B. Kaĭgorodov
published in: Algebra and Logic
publication date: 2012-12-11T00:00:00Z
review text: In this short paper the author states that the following two theorems hold true. Theorem 1. A simple binary Mal'tsev algebra \(M_7\) (a ternary Mal'tsev algebra \(M_8\)) does not have nontrivial 3-ary (resp. 4-ary) derivations. Theorem 2. Let \((f_0, f_1, \ldots, f_n)\) be an \((n+1)\)-ary derivation of a simple finite-dimensional \(n\)-ary Filippov algebra over an algebraically closed field of characteristic zero. Then \[ (f_0, f_1, \ldots, f_n)=\left(\sum_{j=1}^n h_j\cdot \text{id}, h_1\cdot \text{id},\ldots,h_n\cdot \text{id}\right)+(d_0,d,\ldots,d) \] and \(\frac{\text{tr}([d_0])}n E-[d_0]^T=[d]\), where \([d_0]\) and \([d]\) are matrices of linear transformations \(d_0\) and \(d\)
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 17A42
Mathematics Subject Classification ID: 17A36
Mathematics Subject Classification ID: 17D10
Mathematics Subject Classification ID: 08A62
zbMATH DE Number: 6115019
MaRDI profile type: Publication
full work available at URL: s10469-011-9157-2
OpenAlex ID: W2079642971
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cites work: Q4802801
cites work: Q4302405
DOI: 10.1007/S10469-011-9157-2
description: scientific article; zbMATH DE number 6115019