Geodesic
Local and 2-Local Derivations on Lie Matrix Rings over Commutative Involutive Rings
Journal of Lie theory, Tome 32 (2022) no. 4, pp. 1053-1071
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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.
Classification : 17B40, 17B65, 46L57, 46L70, 46K70
Mots-clés : Inner Lie derivation, 2-local Lie derivation, Lie ring, Lie algebras, Lie ring of skew-adjoint matrices 
@article{JLT_2022_32_4_JLT_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},
     url = {http://geodesic.mathdoc.fr/item/JLT_2022_32_4_JLT_2022_32_4_a7/}
}
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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, Tome 32 (2022) no. 4, pp. 1053-1071. http://geodesic.mathdoc.fr/item/JLT_2022_32_4_JLT_2022_32_4_a7/