Minimal Matrix Representations for Six-Dimensional Nilpotent Lie Algebras

Authors

Ryad Ghanam, Virginia Commonwealth University in QatarFollow
Gerard Thompson, University of Toledo

Document Type

Article

Original Publication Date

2018

Journal/Book/Conference Title

Mathematica Æterna

Volume

8

Issue

3

First Page

113

Last Page

138

Comments

Originally published at https://www.longdom.org/abstract/minimal-matrix-representations-for-sixdimensional-nilpotent-lie-algebras-4810.html

Funded in part by the VCU Libraries Open Access Publishing Fund.

Date of Submission

October 2019

Abstract

This paper is concerned with finding minimal dimension linear representations for six-dimensional real, indecomposable nilpotent Lie algebras. It is known that all such Lie algebras can be represented in gl(6, R). After discussing the classification of the 24 such Lie algebras, it is shown that only one algebra can be represented in gl(4, R). A Theorem is then presented that shows that 13 of the algebras can be represented in gl(5, R). The special case of filiform Lie algebras is considered, of which there are five, and it is shown that each of them can be represented in gl(6, R) and not gl(5, R). Of the remaining five algebras, four of them can be represented minimally in gl(5, R). That leaves one difficult case that is treated in detail in an Appendix.

Rights

This article is under the terms of the Creative Commons Attribution License.

Is Part Of

VCUQatar Publications