Derivations and centroids of finite dimensional dialgebras

The thesis deals with the derivations, generalized derivations and centroids of associative and diassociative algebras. In all the cases, we give an algorithm to find the derivation algebras. The algorithm is applied to compute the derivations of low dimensional diassociative algebras. Having found...

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Main Author:	Mohamed, Mohamed Abubakar Hagi
Format:	Thesis
Language:	English
Published:	2016
Subjects:	Algebra Dimensional analysis Algorithms
Online Access:	http://psasir.upm.edu.my/id/eprint/75480/1/FS%202016%2019%20-%20IR.pdf
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id	my-upm-ir.75480
record_format	uketd_dc
spelling	my-upm-ir.754802019-10-18T07:51:03Z Derivations and centroids of finite dimensional dialgebras 2016-07 Mohamed, Mohamed Abubakar Hagi The thesis deals with the derivations, generalized derivations and centroids of associative and diassociative algebras. In all the cases, we give an algorithm to find the derivation algebras. The algorithm is applied to compute the derivations of low dimensional diassociative algebras. Having found the derivations, we determine those diassociative algebras that are characteristically nilpotent. Some basic properties of derivations in terms of left and right multiplication operators are also given for each case. We introduce a generalization of derivation of diassociative algebras and study its properties. The generalization of derivation depends on parameters (a;b; g); we specify all possible values of the parameters. All of the generalized derivations of low-dimensional complex diassociative algebras are given. We also introduce the concept of centroid for associative and diassociative algebras and study some of their properties. An algorithm to find centroids of algebras is given as well. The algorithm is then applied to determine the centroids of low dimensional algebras. Algebra Dimensional analysis Algorithms 2016-07 Thesis http://psasir.upm.edu.my/id/eprint/75480/ http://psasir.upm.edu.my/id/eprint/75480/1/FS%202016%2019%20-%20IR.pdf text en public doctoral Universiti Putra Malaysia Algebra Dimensional analysis Algorithms
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Algebra Dimensional analysis Algorithms
spellingShingle	Algebra Dimensional analysis Algorithms Mohamed, Mohamed Abubakar Hagi Derivations and centroids of finite dimensional dialgebras
description	The thesis deals with the derivations, generalized derivations and centroids of associative and diassociative algebras. In all the cases, we give an algorithm to find the derivation algebras. The algorithm is applied to compute the derivations of low dimensional diassociative algebras. Having found the derivations, we determine those diassociative algebras that are characteristically nilpotent. Some basic properties of derivations in terms of left and right multiplication operators are also given for each case. We introduce a generalization of derivation of diassociative algebras and study its properties. The generalization of derivation depends on parameters (a;b; g); we specify all possible values of the parameters. All of the generalized derivations of low-dimensional complex diassociative algebras are given. We also introduce the concept of centroid for associative and diassociative algebras and study some of their properties. An algorithm to find centroids of algebras is given as well. The algorithm is then applied to determine the centroids of low dimensional algebras.
format	Thesis
qualification_level	Doctorate
author	Mohamed, Mohamed Abubakar Hagi
author_facet	Mohamed, Mohamed Abubakar Hagi
author_sort	Mohamed, Mohamed Abubakar Hagi
title	Derivations and centroids of finite dimensional dialgebras
title_short	Derivations and centroids of finite dimensional dialgebras
title_full	Derivations and centroids of finite dimensional dialgebras
title_fullStr	Derivations and centroids of finite dimensional dialgebras
title_full_unstemmed	Derivations and centroids of finite dimensional dialgebras
title_sort	derivations and centroids of finite dimensional dialgebras
granting_institution	Universiti Putra Malaysia
publishDate	2016
url	http://psasir.upm.edu.my/id/eprint/75480/1/FS%202016%2019%20-%20IR.pdf
_version_	1747813056671383552

Derivations and centroids of finite dimensional dialgebras

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