Geodesic
Local and 2-Local Derivations on Lie Matrix Rings over Commutative Involutive Rings
Shavkat A. Ayupov1, 2 ; Farhodjon N. Arzikulov1, 3 ; Sandorbek M. Umrzaqov3
1V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
2National University of Uzbekistan, Tashkent, Uzbekistan
3Andizhan State University, Andizhan, Uzbekistan
Journal of Lie Theory, Tome 32 (2022) no. 4, pp. 1053-1071

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Shavkat A. Ayupov  1 , 2   ; Farhodjon N. Arzikulov  1 , 3   ; Sandorbek M. Umrzaqov  3

1 V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
2 National University of Uzbekistan, Tashkent, Uzbekistan
3 Andizhan State University, Andizhan, Uzbekistan 
Shavkat A. Ayupov; Farhodjon N. Arzikulov; Sandorbek 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/JOLT_2022_32_4_a7/
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     author = {Shavkat A. Ayupov and Farhodjon N. Arzikulov and Sandorbek 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/JOLT_2022_32_4_a7/}
}
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