On primitive Lie algebras
type: Item
instance of: scholarly article
title: On primitive Lie algebras
zbMATH Open document ID: 1282.17006
author: A. A. Kucherov
author: O. A. Pikhtil'kova
author: S. A. Pikhtil'kov
published in: Journal of Mathematical Sciences (New York)
publication date: 2013-04-23T00:00:00Z
review text: The authors give sufficient conditions for Lie algebra primitiveness and examples of primitive Lie algebras and nonprimitive Lie algebras. They prove the following theorems. Theorem 1. Let \(L\) be an Artinian Lie algebra over a field. Let \(L\) have a unique minimal ideal. Then the Lie algebra \(L\) is primitive. Theorem 2. Let \(L_1\) and \(L_2\) be primitive algebras having faithful irreducible representations \(\varphi_i : L_i\to M_i\) such that the centroids \(\Delta_i\) of the modules \(M_i\) coincide with the basic field and \(\varphi_i(L_i) \cap \Delta_i = 0\), where \(i = 1, 2\). Then their direct sum \(L_1 \oplus L_2\) is also primitive.
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 17B05
zbMATH DE Number: 6156632
MaRDI profile type: Publication
full work available at URL: s10958-012-1011-0
OpenAlex ID: W2076408150
cites work: Q4761795
cites work: Q5670746
cites work: Triality and Lie algebras of type \(D_4\)
cites work: Q5567970
DOI: 10.1007/S10958-012-1011-0
description: scientific article; zbMATH DE number 6156632