Journal of Lie Theory

no. 4
Local and 2-Local Derivations on Lie Matrix Rings over Commutative Involutive Rings
Journal of Lie Theory, Volume 32 (2022) no. 4, pp. 1053-1071
We prove that every 2-local inner derivation on the Lie ring of skew-adjoint matrices over a commutative *-ring is an inner derivation. We also prove that every 2-local spatial derivation on various Lie algebras of skew-adjoint operator-valued maps on a set is a spatial derivation. We also show that every local spatial derivation on the Lie algebras mentioned above is a derivation.
DOI: 10.5802/jolt.1265
Classification: 17B40, 17B65, 46L57, 46L70, 46K70
Keywords: Inner Lie derivation, 2-local Lie derivation, Lie ring, Lie algebras, Lie ring of skew-adjoint matrices 
@article{JOLT_2022_32_4_a7,
     author = {Sh. A. Ayupov and F. N. Arzikulov and S. M. Umrzaqov},
     title = {Local and {2-Local} {Derivations} on {Lie} {Matrix} {Rings} over {Commutative} {Involutive} {Rings}},
     journal = {Journal of Lie Theory},
     pages = {1053--1071},
     year = {2022},
     volume = {32},
     number = {4},
     doi = {10.5802/jolt.1265},
     zbl = {1521.17035},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1265/}
}
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%A F. N. Arzikulov
%A S. M. Umrzaqov
%T Local and 2-Local Derivations on Lie Matrix Rings over Commutative Involutive Rings
%J Journal of Lie Theory
%D 2022
%P 1053-1071
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%F JOLT_2022_32_4_a7
Sh. A. Ayupov; F. N. Arzikulov; S. M. Umrzaqov. Local and 2-Local Derivations on Lie Matrix Rings over Commutative Involutive Rings. Journal of Lie Theory, Volume 32 (2022) no. 4, pp. 1053-1071. doi: 10.5802/jolt.1265

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