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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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spelling oai:psasir.upm.edu.my:12372 http://psasir.upm.edu.my/id/eprint/12372/ Central Extensions of Nilpotent Lie and Leibniz Algebras 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. 2010-06 Thesis NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/12372/1/IPM_2010_2A.pdf Langari, Mouna Bibi (2010) Central Extensions of Nilpotent Lie and Leibniz Algebras. Masters thesis, Universiti Putra Malaysia. Nilpotent Lie groups Lie algebras English
institution UPM IR
collection UPM IR
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
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
publishDate 2010
url http://psasir.upm.edu.my/id/eprint/12372/1/IPM_2010_2A.pdf
_version_ 1819293605538299904
score 13.4562235

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