Isomorphism classes and invariants of low-dimensional filiform Leibniz algebras
In the paper, we extend the result on classification of a subclass of filiform Leibniz algebras in low dimensions to dimensions seven and eight based on a technique used by Rakhimov and Bekbaev for classification of subclasses which arise from naturally graded non-Lie filiform Leibniz algebras. The...
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| Format: | Article |
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Taylor & Francis
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/34294/ |
| _version_ | 1848847731151339520 |
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| author | Abdulkareem, Abdulafeez Olalekan Sattarovich, Rakhimov Isamiddin Said Husain, Sharifah Kartini |
| author_facet | Abdulkareem, Abdulafeez Olalekan Sattarovich, Rakhimov Isamiddin Said Husain, Sharifah Kartini |
| author_sort | Abdulkareem, Abdulafeez Olalekan |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In the paper, we extend the result on classification of a subclass of filiform Leibniz algebras in low dimensions to dimensions seven and eight based on a technique used by Rakhimov and Bekbaev for classification of subclasses which arise from naturally graded non-Lie filiform Leibniz algebras. The class considered here arises from naturally graded filiform Lie algebras. It contains the class of filiform Lie algebras and consequently, by classifying this subclass, we again re-examine the classification result of filiform Lie algebras. The resulting list of filiform Lie algebras is compared with that given by Ancochéa-Bermúdez and Goze in 1988 and by Gómez, Jiménez-Merchán and Khakimdjanov in 1998. |
| first_indexed | 2025-11-15T09:23:16Z |
| format | Article |
| id | upm-34294 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T09:23:16Z |
| publishDate | 2015 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-342942015-12-10T03:39:50Z http://psasir.upm.edu.my/id/eprint/34294/ Isomorphism classes and invariants of low-dimensional filiform Leibniz algebras Abdulkareem, Abdulafeez Olalekan Sattarovich, Rakhimov Isamiddin Said Husain, Sharifah Kartini In the paper, we extend the result on classification of a subclass of filiform Leibniz algebras in low dimensions to dimensions seven and eight based on a technique used by Rakhimov and Bekbaev for classification of subclasses which arise from naturally graded non-Lie filiform Leibniz algebras. The class considered here arises from naturally graded filiform Lie algebras. It contains the class of filiform Lie algebras and consequently, by classifying this subclass, we again re-examine the classification result of filiform Lie algebras. The resulting list of filiform Lie algebras is compared with that given by Ancochéa-Bermúdez and Goze in 1988 and by Gómez, Jiménez-Merchán and Khakimdjanov in 1998. Taylor & Francis 2015 Article PeerReviewed Abdulkareem, Abdulafeez Olalekan and Sattarovich, Rakhimov Isamiddin and Said Husain, Sharifah Kartini (2015) Isomorphism classes and invariants of low-dimensional filiform Leibniz algebras. Linear and Multilinear Algebra, 63 (11). pp. 2254-2274. ISSN 0308-1087; ESSN: 1563-5139 http://www.tandfonline.com/doi/abs/10.1080/03081087.2014.1001757 10.1080/03081087.2014.1001757 |
| spellingShingle | Abdulkareem, Abdulafeez Olalekan Sattarovich, Rakhimov Isamiddin Said Husain, Sharifah Kartini Isomorphism classes and invariants of low-dimensional filiform Leibniz algebras |
| title | Isomorphism classes and invariants of low-dimensional filiform Leibniz algebras |
| title_full | Isomorphism classes and invariants of low-dimensional filiform Leibniz algebras |
| title_fullStr | Isomorphism classes and invariants of low-dimensional filiform Leibniz algebras |
| title_full_unstemmed | Isomorphism classes and invariants of low-dimensional filiform Leibniz algebras |
| title_short | Isomorphism classes and invariants of low-dimensional filiform Leibniz algebras |
| title_sort | isomorphism classes and invariants of low-dimensional filiform leibniz algebras |
| url | http://psasir.upm.edu.my/id/eprint/34294/ http://psasir.upm.edu.my/id/eprint/34294/ http://psasir.upm.edu.my/id/eprint/34294/ |