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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
Online Access:http://psasir.upm.edu.my/id/eprint/75480/1/FS%202016%2019%20-%20IR.pdf
http://psasir.upm.edu.my/id/eprint/75480/
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spelling my.upm.eprints.754802019-10-18T07:51:03Z http://psasir.upm.edu.my/id/eprint/75480/ Derivations and centroids of finite dimensional dialgebras 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. 2016-07 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/75480/1/FS%202016%2019%20-%20IR.pdf Mohamed, Mohamed Abubakar Hagi (2016) Derivations and centroids of finite dimensional dialgebras. PhD thesis, Universiti Putra Malaysia.
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
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
author Mohamed, Mohamed Abubakar Hagi
spellingShingle Mohamed, Mohamed Abubakar Hagi
Derivations and centroids of finite dimensional dialgebras
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
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/75480/1/FS%202016%2019%20-%20IR.pdf
http://psasir.upm.edu.my/id/eprint/75480/
_version_ 1648738226661228544
score 13.250719

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