On the existence of orthogonal decompositions of the simple Lie algebra of type \(C_3\)
type: Item
instance of: scholarly article
title: On the existence of orthogonal decompositions of the simple Lie algebra of type \(C_3\)
zbMATH Open document ID: 0968.17004
published in: Computer Science Journal of Moldova
publication date: 2001-09-16T00:00:00Z
review text: The paper deals with a simple complex Lie algebra \(C_{3}.\) The possibility to decompose \(C_{3}\) into a direct sum of Cartan subalgebras which are orthogonal to each other with respect to Killing form is explored. In the case of \(C_{3}\) it is necessary to find 7 orthogonal to each other sets of matrices each containing 3 commuting, linearly independent, diagonalizable matrices. The author concentrates on the existence of monomial orthogonal decompositions. An orthogonal decomposition is called monomial if there exists a basis consisting of monomial matrices for each Cartan subalgebra that occurs. A nonsingular matrix is called monomial if it can be written as a product of a diagonal matrix and a permutation matrix. The author proves, using computational methods (Maple), that \(C_{3}\) has no monomial orthogonal decomposition. At the end of the paper Maple scripts are presented.
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 17-08
zbMATH DE Number: 1558145
zbMATH Keywords: simple complex Lie algebra
zbMATH Keywords: Cartan subalgebras
zbMATH Keywords: Killing form
zbMATH Keywords: monomial orthogonal decompositions
zbMATH Keywords: Maple
author: Anna Torstensson
reviewed by: Alexander Rudy
describes a project that uses: Maple
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1558145