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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id	my-upm-ir.67536
record_format	uketd_dc
spelling	my-upm-ir.675362019-03-14T02:06:31Z Classification of second class filiform leibniz algebras in dimension nine 2013-08 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. Logic, Symbolic and mathematical Algebra 2013-08 Thesis http://psasir.upm.edu.my/id/eprint/67536/ http://psasir.upm.edu.my/id/eprint/67536/1/FS%202013%2099%20IR.pdf text en public masters Universiti Putra Malaysia Logic, Symbolic and mathematical Algebra
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
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
qualification_level	Master's degree
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
granting_institution	Universiti Putra Malaysia
publishDate	2013
url	http://psasir.upm.edu.my/id/eprint/67536/1/FS%202013%2099%20IR.pdf
_version_	1747812482347433984

Classification of second class filiform leibniz algebras in dimension nine

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