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Classification of second class filiform leibniz algebras in dimension nine

This study is centered on part of structural property of Leibniz algebras which is classification of a subclass of filiform Leibniz algebras over complex field. The class of filiform Leibniz algebras has been divided into three disjoint classes. The first two subclasses denoted by FLbn and SLb...

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Main Author: Deraman, Fatanah
Format: Thesis
Language:English
Published: 2013
Subjects:
Logic, Symbolic and mathematical
Algebra
Online Access:http://psasir.upm.edu.my/id/eprint/67536/1/FS%202013%2099%20IR.pdf
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spelling oai:psasir.upm.edu.my:67536 http://psasir.upm.edu.my/id/eprint/67536/ Classification of second class filiform leibniz algebras in dimension nine Deraman, Fatanah This study is centered on part of structural property of Leibniz algebras which is classification of a subclass of filiform Leibniz algebras over complex field. The class of filiform Leibniz algebras has been divided into three disjoint classes. The first two subclasses denoted by FLbn and SLbn arise from naturally graded non- Lie filiform Leibniz algebras. The third class, TLbn arises from naturally graded filiform Lie algebras. In particular, the study is focused on the classification prob- lem of second class filiform Leibniz algebras, SLbn. The method employed in the classification is to first construct multiplication table of SLb9. Then, adapted transformation and elementary base change are used to create an isomorphism criterion. From the isomorphism criterion, the isomorphism classes of algebras from SLb9 are deduced. Some of these classes are single orbits while others are parametric family orbits. An invariant algebraic approach is used to describe the parametric family of orbits. As a result, it is concluded that there are 38 families of non-isomorphic classes of algebras in SLb9. This comprises 17 single orbits and 21 parametric families of orbits. 2013-08 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/67536/1/FS%202013%2099%20IR.pdf Deraman, Fatanah (2013) Classification of second class filiform leibniz algebras in dimension nine. Masters thesis, Universiti Putra Malaysia. Logic, Symbolic and mathematical Algebra
institution UPM IR
collection UPM IR
language English
topic Logic, Symbolic and mathematical
Algebra
spellingShingle Logic, Symbolic and mathematical
Algebra
Deraman, Fatanah
Classification of second class filiform leibniz algebras in dimension nine
description This study is centered on part of structural property of Leibniz algebras which is classification of a subclass of filiform Leibniz algebras over complex field. The class of filiform Leibniz algebras has been divided into three disjoint classes. The first two subclasses denoted by FLbn and SLbn arise from naturally graded non- Lie filiform Leibniz algebras. The third class, TLbn arises from naturally graded filiform Lie algebras. In particular, the study is focused on the classification prob- lem of second class filiform Leibniz algebras, SLbn. The method employed in the classification is to first construct multiplication table of SLb9. Then, adapted transformation and elementary base change are used to create an isomorphism criterion. From the isomorphism criterion, the isomorphism classes of algebras from SLb9 are deduced. Some of these classes are single orbits while others are parametric family orbits. An invariant algebraic approach is used to describe the parametric family of orbits. As a result, it is concluded that there are 38 families of non-isomorphic classes of algebras in SLb9. This comprises 17 single orbits and 21 parametric families of orbits.
format Thesis
author Deraman, Fatanah
author_facet Deraman, Fatanah
author_sort Deraman, Fatanah
title Classification of second class filiform leibniz algebras in dimension nine
title_short Classification of second class filiform leibniz algebras in dimension nine
title_full Classification of second class filiform leibniz algebras in dimension nine
title_fullStr Classification of second class filiform leibniz algebras in dimension nine
title_full_unstemmed Classification of second class filiform leibniz algebras in dimension nine
title_sort classification of second class filiform leibniz algebras in dimension nine
publishDate 2013
url http://psasir.upm.edu.my/id/eprint/67536/1/FS%202013%2099%20IR.pdf
_version_ 1819298605801930752
score 13.4562235

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