2-Local derivations on finite-dimensional semi-simple Lie algebras
We prove that every 2-local derivation on a finite-dimensional semi-simple Lie algebra L over an algebraically closed field of characteristic zero is a derivation. We also show that a finite-dimensional nilpotent Lie algebra L with dim L ≥ 2 admits a 2-local derivation which is not a derivation.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/43451/1/2.pdf |
| _version_ | 1825929365406351360 |
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| author | Ayupov, Shavkat Kudaybergenov, Karimbergen Sattarovich, Rakhimov Isamiddin |
| author_facet | Ayupov, Shavkat Kudaybergenov, Karimbergen Sattarovich, Rakhimov Isamiddin |
| author_sort | Ayupov, Shavkat |
| collection | UPM |
| description | We prove that every 2-local derivation on a finite-dimensional semi-simple Lie algebra L over an algebraically closed field of characteristic zero is a derivation. We also show that a finite-dimensional nilpotent Lie algebra L with dim L ≥ 2 admits a 2-local derivation which is not a derivation. |
| first_indexed | 2024-03-06T08:55:42Z |
| format | Article |
| id | upm.eprints-43451 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:55:42Z |
| publishDate | 2015 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | upm.eprints-434512016-05-13T08:14:15Z http://psasir.upm.edu.my/id/eprint/43451/ 2-Local derivations on finite-dimensional semi-simple Lie algebras Ayupov, Shavkat Kudaybergenov, Karimbergen Sattarovich, Rakhimov Isamiddin We prove that every 2-local derivation on a finite-dimensional semi-simple Lie algebra L over an algebraically closed field of characteristic zero is a derivation. We also show that a finite-dimensional nilpotent Lie algebra L with dim L ≥ 2 admits a 2-local derivation which is not a derivation. Elsevier 2015 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/43451/1/2.pdf Ayupov, Shavkat and Kudaybergenov, Karimbergen and Sattarovich, Rakhimov Isamiddin (2015) 2-Local derivations on finite-dimensional semi-simple Lie algebras. Linear Algebra and Its Applications, 474. pp. 1-11. ISSN 0024-3795; ESSN: 1873-1856 10.1016/j.laa.2015.01.016 |
| spellingShingle | Ayupov, Shavkat Kudaybergenov, Karimbergen Sattarovich, Rakhimov Isamiddin 2-Local derivations on finite-dimensional semi-simple Lie algebras |
| title | 2-Local derivations on finite-dimensional semi-simple Lie algebras |
| title_full | 2-Local derivations on finite-dimensional semi-simple Lie algebras |
| title_fullStr | 2-Local derivations on finite-dimensional semi-simple Lie algebras |
| title_full_unstemmed | 2-Local derivations on finite-dimensional semi-simple Lie algebras |
| title_short | 2-Local derivations on finite-dimensional semi-simple Lie algebras |
| title_sort | 2 local derivations on finite dimensional semi simple lie algebras |
| url | http://psasir.upm.edu.my/id/eprint/43451/1/2.pdf |
| work_keys_str_mv | AT ayupovshavkat 2localderivationsonfinitedimensionalsemisimpleliealgebras AT kudaybergenovkarimbergen 2localderivationsonfinitedimensionalsemisimpleliealgebras AT sattarovichrakhimovisamiddin 2localderivationsonfinitedimensionalsemisimpleliealgebras |