Classification of Five-Dimensional Lie Algebras with One-dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra
Motivated by A. Z. Petrov's classification of four-dimensional Lorentzian metrics, we provide an algebraic classification of the isometry-isotropy pairs of four-dimensional pseudo-Riemannian metrics admitting local slices with five-dimensional isometries contained in the Lorentz algebra. A pure...
Main Author: | |
---|---|
Format: | Others |
Published: |
DigitalCommons@USU
2015
|
Subjects: | |
Online Access: | https://digitalcommons.usu.edu/etd/4633 https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=5669&context=etd |
id |
ndltd-UTAHS-oai-digitalcommons.usu.edu-etd-5669 |
---|---|
record_format |
oai_dc |
spelling |
ndltd-UTAHS-oai-digitalcommons.usu.edu-etd-56692019-10-13T05:52:28Z Classification of Five-Dimensional Lie Algebras with One-dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra Rozum, Jordan Motivated by A. Z. Petrov's classification of four-dimensional Lorentzian metrics, we provide an algebraic classification of the isometry-isotropy pairs of four-dimensional pseudo-Riemannian metrics admitting local slices with five-dimensional isometries contained in the Lorentz algebra. A purely Lie algebraic approach is applied with emphasis on the use of Lie theoretic invariants to distinguish invariant algebra-subalgebra pairs. This method yields an algorithm for identifying isometry-isotropy pairs subject to the aforementioned constraints. 2015-05-01T07:00:00Z text application/pdf https://digitalcommons.usu.edu/etd/4633 https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=5669&context=etd Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact Andrew Wesolek (andrew.wesolek@usu.edu). All Graduate Theses and Dissertations DigitalCommons@USU classification five-dimensional lie algebras one-dimensional subalgebras subalgebras lorentz algebra Mathematics |
collection |
NDLTD |
format |
Others
|
sources |
NDLTD |
topic |
classification five-dimensional lie algebras one-dimensional subalgebras subalgebras lorentz algebra Mathematics |
spellingShingle |
classification five-dimensional lie algebras one-dimensional subalgebras subalgebras lorentz algebra Mathematics Rozum, Jordan Classification of Five-Dimensional Lie Algebras with One-dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra |
description |
Motivated by A. Z. Petrov's classification of four-dimensional Lorentzian metrics, we provide an algebraic classification of the isometry-isotropy pairs of four-dimensional pseudo-Riemannian metrics admitting local slices with five-dimensional isometries contained in the Lorentz algebra. A purely Lie algebraic approach is applied with emphasis on the use of Lie theoretic invariants to distinguish invariant algebra-subalgebra pairs. This method yields an algorithm for identifying isometry-isotropy pairs subject to the aforementioned constraints. |
author |
Rozum, Jordan |
author_facet |
Rozum, Jordan |
author_sort |
Rozum, Jordan |
title |
Classification of Five-Dimensional Lie Algebras with One-dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra |
title_short |
Classification of Five-Dimensional Lie Algebras with One-dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra |
title_full |
Classification of Five-Dimensional Lie Algebras with One-dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra |
title_fullStr |
Classification of Five-Dimensional Lie Algebras with One-dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra |
title_full_unstemmed |
Classification of Five-Dimensional Lie Algebras with One-dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra |
title_sort |
classification of five-dimensional lie algebras with one-dimensional subalgebras acting as subalgebras of the lorentz algebra |
publisher |
DigitalCommons@USU |
publishDate |
2015 |
url |
https://digitalcommons.usu.edu/etd/4633 https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=5669&context=etd |
work_keys_str_mv |
AT rozumjordan classificationoffivedimensionalliealgebraswithonedimensionalsubalgebrasactingassubalgebrasofthelorentzalgebra |
_version_ |
1719266891830132736 |