Combinatorial structure associated with low-dimensional filiform leibniz algebras

This thesis is concerned on the studying a graph representation of (n + 1)- dimensional filiform Leibniz algebras. The filiform Leibniz algebras contain three subclasses called first, second and third class that are denoted in dimension n over a field K, by FLbn(K), SLbn(K) and TLbn(K), respec...

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Main Author:	Ahmad Jamri, Ayu Ameliatul Shahilah
Format:	Thesis
Language:	English
Published:	2017
Subjects:	Mathematical statistics Algebra Representations of algebras
Online Access:	http://psasir.upm.edu.my/id/eprint/69419/1/IPM%202018%202%20IR.pdf
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id	my-upm-ir.69419
record_format	uketd_dc
spelling	my-upm-ir.694192019-07-10T00:57:12Z Combinatorial structure associated with low-dimensional filiform leibniz algebras 2017-04 Ahmad Jamri, Ayu Ameliatul Shahilah This thesis is concerned on the studying a graph representation of (n + 1)- dimensional filiform Leibniz algebras. The filiform Leibniz algebras contain three subclasses called first, second and third class that are denoted in dimension n over a field K, by FLbn(K), SLbn(K) and TLbn(K), respectively. This research deals with combinatorial structures associated with FLbn(K) and SLbn(K). Therefore, an algorithm is defined in order to construct such structures associated with filiform Leibniz algebras. By using the table of multiplication of filiform Leibniz algebras, an algorithm for the combinatorial structures associated with filiform Leibniz algebras will be obtained. Next, the structural properties of the combinatorial structure will be constructed to show the non-isomorphism between two classes of filiform Leibniz algebras in such a way of graph theory. Hence, some propositions on combinatorial structures regarding number of vertices and edge, components, degree of vertices, diameter and degree sequences are given. Besides that, an algorithm will be used on association the combinatorial structures with the isomorphism classes of FLbn(K) and SLbn(K). Thus, any two isomorphism classes of FLbn(K) or SLbn(K) are non-isomorphic using combinatorial structures. Mathematical statistics Algebra Representations of algebras 2017-04 Thesis http://psasir.upm.edu.my/id/eprint/69419/ http://psasir.upm.edu.my/id/eprint/69419/1/IPM%202018%202%20IR.pdf text en public masters Universiti Putra Malaysia Mathematical statistics Algebra Representations of algebras
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Mathematical statistics Algebra Representations of algebras
spellingShingle	Mathematical statistics Algebra Representations of algebras Ahmad Jamri, Ayu Ameliatul Shahilah Combinatorial structure associated with low-dimensional filiform leibniz algebras
description	This thesis is concerned on the studying a graph representation of (n + 1)- dimensional filiform Leibniz algebras. The filiform Leibniz algebras contain three subclasses called first, second and third class that are denoted in dimension n over a field K, by FLbn(K), SLbn(K) and TLbn(K), respectively. This research deals with combinatorial structures associated with FLbn(K) and SLbn(K). Therefore, an algorithm is defined in order to construct such structures associated with filiform Leibniz algebras. By using the table of multiplication of filiform Leibniz algebras, an algorithm for the combinatorial structures associated with filiform Leibniz algebras will be obtained. Next, the structural properties of the combinatorial structure will be constructed to show the non-isomorphism between two classes of filiform Leibniz algebras in such a way of graph theory. Hence, some propositions on combinatorial structures regarding number of vertices and edge, components, degree of vertices, diameter and degree sequences are given. Besides that, an algorithm will be used on association the combinatorial structures with the isomorphism classes of FLbn(K) and SLbn(K). Thus, any two isomorphism classes of FLbn(K) or SLbn(K) are non-isomorphic using combinatorial structures.
format	Thesis
qualification_level	Master's degree
author	Ahmad Jamri, Ayu Ameliatul Shahilah
author_facet	Ahmad Jamri, Ayu Ameliatul Shahilah
author_sort	Ahmad Jamri, Ayu Ameliatul Shahilah
title	Combinatorial structure associated with low-dimensional filiform leibniz algebras
title_short	Combinatorial structure associated with low-dimensional filiform leibniz algebras
title_full	Combinatorial structure associated with low-dimensional filiform leibniz algebras
title_fullStr	Combinatorial structure associated with low-dimensional filiform leibniz algebras
title_full_unstemmed	Combinatorial structure associated with low-dimensional filiform leibniz algebras
title_sort	combinatorial structure associated with low-dimensional filiform leibniz algebras
granting_institution	Universiti Putra Malaysia
publishDate	2017
url	http://psasir.upm.edu.my/id/eprint/69419/1/IPM%202018%202%20IR.pdf
_version_	1747812694822486016

Combinatorial structure associated with low-dimensional filiform leibniz algebras

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