Lie triple derivations of dihedron algebra
Let K be a 2-torsion free unital ring and D(K) be dihedron algebra over K. In the present article, we prove that every Lie triple derivation of D(K) can be written as the sum of the Lie triple derivation of K, Jordan triple derivation of K, and some inner derivation of D. We also prove that a genera...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2023-09-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2023.1179246/full |
| _version_ | 1797670687636193280 |
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| author | Minahal Arshad Muhammad Mobeen Munir |
| author_facet | Minahal Arshad Muhammad Mobeen Munir |
| author_sort | Minahal Arshad |
| collection | DOAJ |
| description | Let K be a 2-torsion free unital ring and D(K) be dihedron algebra over K. In the present article, we prove that every Lie triple derivation of D(K) can be written as the sum of the Lie triple derivation of K, Jordan triple derivation of K, and some inner derivation of D. We also prove that a generalized Lie triple derivation ϱ:D(K)→D(K) associated with the Lie triple derivation h:D(K)→D(K) exists if ϱ can be represented in the form ϱ(τ) = h(τ) + λτ, where λ lies in the center of D(K). We finally conclude that to obtain the complete algebra of the Lie triple derivation and generalized Lie triple of D(K), we first need to find the Lie triple derivation and Jordan triple derivation of K. |
| first_indexed | 2024-03-11T21:04:07Z |
| format | Article |
| id | doaj.art-e98d558e05f740f49c36a6f25975ca1a |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-03-11T21:04:07Z |
| publishDate | 2023-09-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-e98d558e05f740f49c36a6f25975ca1a2023-09-29T16:27:07ZengFrontiers Media S.A.Frontiers in Physics2296-424X2023-09-011110.3389/fphy.2023.11792461179246Lie triple derivations of dihedron algebraMinahal ArshadMuhammad Mobeen MunirLet K be a 2-torsion free unital ring and D(K) be dihedron algebra over K. In the present article, we prove that every Lie triple derivation of D(K) can be written as the sum of the Lie triple derivation of K, Jordan triple derivation of K, and some inner derivation of D. We also prove that a generalized Lie triple derivation ϱ:D(K)→D(K) associated with the Lie triple derivation h:D(K)→D(K) exists if ϱ can be represented in the form ϱ(τ) = h(τ) + λτ, where λ lies in the center of D(K). We finally conclude that to obtain the complete algebra of the Lie triple derivation and generalized Lie triple of D(K), we first need to find the Lie triple derivation and Jordan triple derivation of K.https://www.frontiersin.org/articles/10.3389/fphy.2023.1179246/fulldihedron ringLie triple derivationsgeneralized Lie triple derivationsJordan triple derivationsAMS subject classifications: 16W25Lie algebras |
| spellingShingle | Minahal Arshad Muhammad Mobeen Munir Lie triple derivations of dihedron algebra Frontiers in Physics dihedron ring Lie triple derivations generalized Lie triple derivations Jordan triple derivations AMS subject classifications: 16W25 Lie algebras |
| title | Lie triple derivations of dihedron algebra |
| title_full | Lie triple derivations of dihedron algebra |
| title_fullStr | Lie triple derivations of dihedron algebra |
| title_full_unstemmed | Lie triple derivations of dihedron algebra |
| title_short | Lie triple derivations of dihedron algebra |
| title_sort | lie triple derivations of dihedron algebra |
| topic | dihedron ring Lie triple derivations generalized Lie triple derivations Jordan triple derivations AMS subject classifications: 16W25 Lie algebras |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2023.1179246/full |
| work_keys_str_mv | AT minahalarshad lietriplederivationsofdihedronalgebra AT muhammadmobeenmunir lietriplederivationsofdihedronalgebra |