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...

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Main Author:	Rozum, Jordan
Format:	Others
Published:	DigitalCommons@USU 2015
Subjects:	classification five-dimensional lie algebras one-dimensional subalgebras subalgebras lorentz algebra Mathematics
Online Access:	https://digitalcommons.usu.edu/etd/4633 https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=5669&context=etd

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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

Classification of Five-Dimensional Lie Algebras with One-dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra

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