Quaternionic Lie algebras
type: Item
instance of: scholarly article
title: Quaternionic Lie algebras
zbMATH Open document ID: 0548.17004
DOI: 10.1016/0024-3795(84)90033-8
author: Rolf Farnsteiner
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: Let k be a field of characteristic not equal to 2, and let L be a finite field extension of k. Then a Lie algebra G is quaternionic if there is a quaternion division algebra Q over L such that G is isomorphic to the k- Lie-algebra \(Q^-/L1\). The main theorem of the paper gives equivalent conditions for a finite-dimensional Lie algebra over a perfect field k to be quaternionic.
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 17A35
zbMATH DE Number: 3873557
zbMATH Keywords: quaternionic Lie algebra
zbMATH Keywords: central quotient
zbMATH Keywords: simple semiabelian
zbMATH Keywords: Cartan subalgebras
zbMATH Keywords: Fitting decomposition
zbMATH Keywords: ad-semisimple
zbMATH Keywords: characteristic not two
zbMATH Keywords: quaternion division algebra
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90033-8
OpenAlex ID: W1990149960
Wikidata QID: Q115364360
cites work: On ad-semisimple Lie algebras
cites work: On the structure of simple-semiabelian Lie algebras
cites work: Q5732712
description: scientific article; zbMATH DE number 3873557