Central Extensions of Nilpotent Lie and Leibniz Algebras

This thesis is concerned with the central extensions of nilpotent Lie and Leibniz algebras. The researcher has used the Skjelbred and Sund's method to construct all the 6¡dimensional non-isomorphic Lie algebras over complex numbers. Skjelbred and Sund have published in 1977 their method of c...

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Main Author:	Langari, Mouna Bibi
Format:	Thesis
Language:	English English
Published:	2010
Subjects:	Nilpotent Lie groups Lie algebras
Online Access:	http://psasir.upm.edu.my/id/eprint/12372/1/IPM_2010_2A.pdf
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id	my-upm-ir.12372
record_format	uketd_dc
spelling	my-upm-ir.123722013-05-27T07:51:54Z Central Extensions of Nilpotent Lie and Leibniz Algebras 2010-06 Langari, Mouna Bibi This thesis is concerned with the central extensions of nilpotent Lie and Leibniz algebras. The researcher has used the Skjelbred and Sund's method to construct all the 6¡dimensional non-isomorphic Lie algebras over complex numbers. Skjelbred and Sund have published in 1977 their method of constructing all nilpotent Lie algebras of dimension n introducing those algebras of dimension < n, and their automorphism groups. The deployed method in classifying nilpotent Lie algebras for dimension n is necessarily comprised of two main steps. For the frist step, a plausibly redundant list of Lie algebras was confirmed which included all n-dimensional nilpotent Lie algebras. The next step is to discard the isomorphic copies generated from the list of Lie algebras. By then, the n¡dimensional nilpotent Lie algebras are confirmed as central extension of nilpotent Lie algebras for smaller dimensions. As the result, the action of the automorphism group is deployed to drastically decrease the number of isomorphic Lie algebras which may appear in the final list. The maple program is by then deployed to discard the final isomorphic copies from the calculation. Based on the elaborated method, the researcher must and center of Lie algebras then drived algebras. In order to locate a basis for second cohomology group of Lie algebras, the researcher must locate cocycles as well as coboundary. Further, there is the requirement to locate the most appropriate action for finding orbits. By then, every orbit will submit a representative that is illustrated by 0. Nilpotent Lie groups Lie algebras 2010-06 Thesis http://psasir.upm.edu.my/id/eprint/12372/ http://psasir.upm.edu.my/id/eprint/12372/1/IPM_2010_2A.pdf application/pdf en public masters Universiti Putra Malaysia Nilpotent Lie groups Lie algebras Institute For Mathematical Research English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Nilpotent Lie groups Lie algebras
spellingShingle	Nilpotent Lie groups Lie algebras Langari, Mouna Bibi Central Extensions of Nilpotent Lie and Leibniz Algebras
description	This thesis is concerned with the central extensions of nilpotent Lie and Leibniz algebras. The researcher has used the Skjelbred and Sund's method to construct all the 6¡dimensional non-isomorphic Lie algebras over complex numbers. Skjelbred and Sund have published in 1977 their method of constructing all nilpotent Lie algebras of dimension n introducing those algebras of dimension < n, and their automorphism groups. The deployed method in classifying nilpotent Lie algebras for dimension n is necessarily comprised of two main steps. For the frist step, a plausibly redundant list of Lie algebras was confirmed which included all n-dimensional nilpotent Lie algebras. The next step is to discard the isomorphic copies generated from the list of Lie algebras. By then, the n¡dimensional nilpotent Lie algebras are confirmed as central extension of nilpotent Lie algebras for smaller dimensions. As the result, the action of the automorphism group is deployed to drastically decrease the number of isomorphic Lie algebras which may appear in the final list. The maple program is by then deployed to discard the final isomorphic copies from the calculation. Based on the elaborated method, the researcher must and center of Lie algebras then drived algebras. In order to locate a basis for second cohomology group of Lie algebras, the researcher must locate cocycles as well as coboundary. Further, there is the requirement to locate the most appropriate action for finding orbits. By then, every orbit will submit a representative that is illustrated by 0.
format	Thesis
qualification_level	Master's degree
author	Langari, Mouna Bibi
author_facet	Langari, Mouna Bibi
author_sort	Langari, Mouna Bibi
title	Central Extensions of Nilpotent Lie and Leibniz Algebras
title_short	Central Extensions of Nilpotent Lie and Leibniz Algebras
title_full	Central Extensions of Nilpotent Lie and Leibniz Algebras
title_fullStr	Central Extensions of Nilpotent Lie and Leibniz Algebras
title_full_unstemmed	Central Extensions of Nilpotent Lie and Leibniz Algebras
title_sort	central extensions of nilpotent lie and leibniz algebras
granting_institution	Universiti Putra Malaysia
granting_department	Institute For Mathematical Research
publishDate	2010
url	http://psasir.upm.edu.my/id/eprint/12372/1/IPM_2010_2A.pdf
_version_	1747811359528058880

Central Extensions of Nilpotent Lie and Leibniz Algebras

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