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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| Format: | Thesis |
| Language: | English |
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2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/52104/ http://psasir.upm.edu.my/id/eprint/52104/1/IPM%202014%204RR.pdf |
| _version_ | 1848852014519287808 |
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| author | Abdulkareem, Abdulafeez Olalekan |
| author_facet | Abdulkareem, Abdulafeez Olalekan |
| author_sort | Abdulkareem, Abdulafeez Olalekan |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T10:31:21Z |
| format | Thesis |
| id | upm-52104 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:31:21Z |
| publishDate | 2014 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-521042017-05-02T04:05:11Z http://psasir.upm.edu.my/id/eprint/52104/ Classification of a subclass of filiform Leibniz algebra 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. 2014-05 Thesis NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/52104/1/IPM%202014%204RR.pdf Abdulkareem, Abdulafeez Olalekan (2014) Classification of a subclass of filiform Leibniz algebra. Masters thesis, Universiti Putra Malaysia. Mathematical statistics Representations of algebras Algebra |
| spellingShingle | Mathematical statistics Representations of algebras Algebra Abdulkareem, Abdulafeez Olalekan Classification of a subclass of filiform Leibniz algebra |
| title | 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_short | Classification of a subclass of filiform Leibniz algebra |
| title_sort | classification of a subclass of filiform leibniz algebra |
| topic | Mathematical statistics Representations of algebras Algebra |
| url | http://psasir.upm.edu.my/id/eprint/52104/ http://psasir.upm.edu.my/id/eprint/52104/1/IPM%202014%204RR.pdf |