Rigidity of some classes of Lie algebras in connection to Leibniz algebras
In this paper we focus on algebraic aspects of contractions of Lie and Leibniz algebras. The rigidity of algebras plays an important role in the study of their varieties. The rigid algebras generate the irreducible components of this variety. We deal with Leibniz algebras which are generalizations o...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
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AIP Publishing LLC
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/35278/ http://psasir.upm.edu.my/id/eprint/35278/1/Rigidity%20of%20some%20classes%20of%20Lie%20algebras%20in%20connection%20to%20Leibniz%20algebras.pdf |
| _version_ | 1848848010165878784 |
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| author | Abdulkareem, Abdulafeez Olalekan Rakhimov, Isamiddin Sattarovich Said Husain, Sharifah Kartini |
| author_facet | Abdulkareem, Abdulafeez Olalekan Rakhimov, Isamiddin Sattarovich Said Husain, Sharifah Kartini |
| author_sort | Abdulkareem, Abdulafeez Olalekan |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper we focus on algebraic aspects of contractions of Lie and Leibniz algebras. The rigidity of algebras plays an important role in the study of their varieties. The rigid algebras generate the irreducible components of this variety. We deal with Leibniz algebras which are generalizations of Lie algebras. In Lie algebras case, there are different kind of rigidities (rigidity, absolutely rigidity, geometric rigidity, e.t.c.). We explore the relations of these rigidities with Leibniz algebra rigidity. Necessary conditions for a Lie algebra to be Leibniz rigid are discussed. |
| first_indexed | 2025-11-15T09:27:42Z |
| format | Conference or Workshop Item |
| id | upm-35278 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:27:42Z |
| publishDate | 2013 |
| publisher | AIP Publishing LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-352782016-10-12T03:47:05Z http://psasir.upm.edu.my/id/eprint/35278/ Rigidity of some classes of Lie algebras in connection to Leibniz algebras Abdulkareem, Abdulafeez Olalekan Rakhimov, Isamiddin Sattarovich Said Husain, Sharifah Kartini In this paper we focus on algebraic aspects of contractions of Lie and Leibniz algebras. The rigidity of algebras plays an important role in the study of their varieties. The rigid algebras generate the irreducible components of this variety. We deal with Leibniz algebras which are generalizations of Lie algebras. In Lie algebras case, there are different kind of rigidities (rigidity, absolutely rigidity, geometric rigidity, e.t.c.). We explore the relations of these rigidities with Leibniz algebra rigidity. Necessary conditions for a Lie algebra to be Leibniz rigid are discussed. AIP Publishing LLC 2013 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/35278/1/Rigidity%20of%20some%20classes%20of%20Lie%20algebras%20in%20connection%20to%20Leibniz%20algebras.pdf Abdulkareem, Abdulafeez Olalekan and Rakhimov, Isamiddin Sattarovich and Said Husain, Sharifah Kartini (2013) Rigidity of some classes of Lie algebras in connection to Leibniz algebras. In: 21st National Symposium on Mathematical Sciences (SKSM21), 6-8 Nov. 2013, Penang, Malaysia. (pp. 702-707). 10.1063/1.4887675 |
| spellingShingle | Abdulkareem, Abdulafeez Olalekan Rakhimov, Isamiddin Sattarovich Said Husain, Sharifah Kartini Rigidity of some classes of Lie algebras in connection to Leibniz algebras |
| title | Rigidity of some classes of Lie algebras in connection to Leibniz algebras |
| title_full | Rigidity of some classes of Lie algebras in connection to Leibniz algebras |
| title_fullStr | Rigidity of some classes of Lie algebras in connection to Leibniz algebras |
| title_full_unstemmed | Rigidity of some classes of Lie algebras in connection to Leibniz algebras |
| title_short | Rigidity of some classes of Lie algebras in connection to Leibniz algebras |
| title_sort | rigidity of some classes of lie algebras in connection to leibniz algebras |
| url | http://psasir.upm.edu.my/id/eprint/35278/ http://psasir.upm.edu.my/id/eprint/35278/ http://psasir.upm.edu.my/id/eprint/35278/1/Rigidity%20of%20some%20classes%20of%20Lie%20algebras%20in%20connection%20to%20Leibniz%20algebras.pdf |