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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| Format: | Thesis |
| Language: | English |
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2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/75480/1/FS%202016%2019%20-%20IR.pdf |
| _version_ | 1796979864274731008 |
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| author | Mohamed, Mohamed Abubakar Hagi |
| author_facet | Mohamed, Mohamed Abubakar Hagi |
| author_sort | Mohamed, Mohamed Abubakar Hagi |
| collection | UPM |
| 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. |
| first_indexed | 2024-03-06T10:15:09Z |
| format | Thesis |
| id | upm.eprints-75480 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T10:15:09Z |
| publishDate | 2016 |
| record_format | dspace |
| spelling | 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. Doctoral thesis, Universiti Putra Malaysia. Algebra Dimensional analysis Algorithms |
| spellingShingle | Algebra Dimensional analysis Algorithms Mohamed, Mohamed Abubakar Hagi Derivations and centroids of finite dimensional dialgebras |
| title | 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_short | Derivations and centroids of finite dimensional dialgebras |
| title_sort | derivations and centroids of finite dimensional dialgebras |
| topic | Algebra Dimensional analysis Algorithms |
| url | http://psasir.upm.edu.my/id/eprint/75480/1/FS%202016%2019%20-%20IR.pdf |
| work_keys_str_mv | AT mohamedmohamedabubakarhagi derivationsandcentroidsoffinitedimensionaldialgebras |