Classification of a subclass of filiform Leibniz algebra

This study centers on isomorphism classes and invariants of a subclass of filiform Leibniz algebras over complex field. The subclass of filiform Leibniz algebras considered arises from naturally graded filiform Lie algebras. It has been denoted by TLbn in a fixed dimension n. It is noted that dimens...

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Main Author:	Abdulkareem, Abdulafeez Olalekan
Format:	Thesis
Language:	English
Published:	2014
Subjects:	Mathematical statistics Representations of algebras Algebra
Online Access:	http://psasir.upm.edu.my/id/eprint/52104/1/IPM%202014%204RR.pdf
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id	my-upm-ir.52104
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spelling	my-upm-ir.521042017-05-02T04:05:11Z Classification of a subclass of filiform Leibniz algebra 2014-05 Abdulkareem, Abdulafeez Olalekan This study centers on isomorphism classes and invariants of a subclass of filiform Leibniz algebras over complex field. The subclass of filiform Leibniz algebras considered arises from naturally graded filiform Lie algebras. It has been denoted by TLbn in a fixed dimension n. It is noted that dimensional filiform Lie algebras are in TLbn. The intent with this study is to find the classification of third class of filiform Leibniz algebras in dimensions 7 and 8. The classification is carried out by first choosing adapted basis, then construct appropriate multiplication table of the said basis. From the multiplication table, isomorphism criterion is set up using adapted linear transformation and elementary base change. With respect to the condition on the structure constants in adapted basis, difierent disjoint subsets of algebras in TLb7 and TLb8 are obtained. Some of these subsets are single orbits while others are represented as a union of parametric family of orbits. In parametric families of case,the invariants that characterize the parameter in the orbits are given. The filiform Lie algebras in each dimension are specified. Mathematical statistics Representations of algebras Algebra 2014-05 Thesis http://psasir.upm.edu.my/id/eprint/52104/ http://psasir.upm.edu.my/id/eprint/52104/1/IPM%202014%204RR.pdf application/pdf en public masters Universiti Putra Malaysia Mathematical statistics Representations of algebras Algebra
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Mathematical statistics Representations of algebras Algebra
spellingShingle	Mathematical statistics Representations of algebras Algebra Abdulkareem, Abdulafeez Olalekan Classification of a subclass of filiform Leibniz algebra
description	This study centers on isomorphism classes and invariants of a subclass of filiform Leibniz algebras over complex field. The subclass of filiform Leibniz algebras considered arises from naturally graded filiform Lie algebras. It has been denoted by TLbn in a fixed dimension n. It is noted that dimensional filiform Lie algebras are in TLbn. The intent with this study is to find the classification of third class of filiform Leibniz algebras in dimensions 7 and 8. The classification is carried out by first choosing adapted basis, then construct appropriate multiplication table of the said basis. From the multiplication table, isomorphism criterion is set up using adapted linear transformation and elementary base change. With respect to the condition on the structure constants in adapted basis, difierent disjoint subsets of algebras in TLb7 and TLb8 are obtained. Some of these subsets are single orbits while others are represented as a union of parametric family of orbits. In parametric families of case,the invariants that characterize the parameter in the orbits are given. The filiform Lie algebras in each dimension are specified.
format	Thesis
qualification_level	Master's degree
author	Abdulkareem, Abdulafeez Olalekan
author_facet	Abdulkareem, Abdulafeez Olalekan
author_sort	Abdulkareem, Abdulafeez Olalekan
title	Classification of a subclass of filiform Leibniz algebra
title_short	Classification of a subclass of filiform Leibniz algebra
title_full	Classification of a subclass of filiform Leibniz algebra
title_fullStr	Classification of a subclass of filiform Leibniz algebra
title_full_unstemmed	Classification of a subclass of filiform Leibniz algebra
title_sort	classification of a subclass of filiform leibniz algebra
granting_institution	Universiti Putra Malaysia
publishDate	2014
url	http://psasir.upm.edu.my/id/eprint/52104/1/IPM%202014%204RR.pdf
_version_	1747812091941617664

Classification of a subclass of filiform Leibniz algebra

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