Local Lie derivations of generalized matrix algebras
In this paper, we investigate local Lie derivations of a certain class of generalized matrix algebras and show that, under certain conditions, every local Lie derivation of a generalized matrix algebra is a sum of a derivation and a linear central-valued map vanishing on each commutator. The main re...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023349?viewType=HTML |
| _version_ | 1811176140116590592 |
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| author | Dan Liu Jianhua Zhang Mingliang Song |
| author_facet | Dan Liu Jianhua Zhang Mingliang Song |
| author_sort | Dan Liu |
| collection | DOAJ |
| description | In this paper, we investigate local Lie derivations of a certain class of generalized matrix algebras and show that, under certain conditions, every local Lie derivation of a generalized matrix algebra is a sum of a derivation and a linear central-valued map vanishing on each commutator. The main result is then applied to full matrix algebras and unital simple algebras with nontrivial idempotents. |
| first_indexed | 2024-04-10T19:47:22Z |
| format | Article |
| id | doaj.art-64dca0fd0c00455aaf9b08f640a1bf47 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T19:47:22Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-64dca0fd0c00455aaf9b08f640a1bf472023-01-29T02:40:25ZengAIMS PressAIMS Mathematics2473-69882023-01-01836900691210.3934/math.2023349Local Lie derivations of generalized matrix algebrasDan Liu 0Jianhua Zhang1Mingliang Song21. School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing 210013, China2. College of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710062, China1. School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing 210013, ChinaIn this paper, we investigate local Lie derivations of a certain class of generalized matrix algebras and show that, under certain conditions, every local Lie derivation of a generalized matrix algebra is a sum of a derivation and a linear central-valued map vanishing on each commutator. The main result is then applied to full matrix algebras and unital simple algebras with nontrivial idempotents.https://www.aimspress.com/article/doi/10.3934/math.2023349?viewType=HTMLlocal lie derivationlie derivationgeneralized matrix algebrafull matrix algebra |
| spellingShingle | Dan Liu Jianhua Zhang Mingliang Song Local Lie derivations of generalized matrix algebras AIMS Mathematics local lie derivation lie derivation generalized matrix algebra full matrix algebra |
| title | Local Lie derivations of generalized matrix algebras |
| title_full | Local Lie derivations of generalized matrix algebras |
| title_fullStr | Local Lie derivations of generalized matrix algebras |
| title_full_unstemmed | Local Lie derivations of generalized matrix algebras |
| title_short | Local Lie derivations of generalized matrix algebras |
| title_sort | local lie derivations of generalized matrix algebras |
| topic | local lie derivation lie derivation generalized matrix algebra full matrix algebra |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023349?viewType=HTML |
| work_keys_str_mv | AT danliu localliederivationsofgeneralizedmatrixalgebras AT jianhuazhang localliederivationsofgeneralizedmatrixalgebras AT mingliangsong localliederivationsofgeneralizedmatrixalgebras |