Journal of Lie Theory 32 (2022), No. 4, 1053--1071
Copyright Heldermann Verlag 2022
Local and 2-Local Derivations on Lie Matrix Rings over Commutative Involutive Rings
Shavkat A. Ayupov
V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
and: National University of Uzbekistan, Tashkent, Uzbekistan
shavkat.ayupov@mathinst.uz
Farhodjon N. Arzikulov
V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
and: Andizhan State University, Andizhan, Uzbekistan
arzikulovfn@rambler.ru
Sandorbek M. Umrzaqov
Andizhan State University, Andizhan, Uzbekistan
sardor.umrzaqov1986@gmail.com
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.
Keywords: Inner Lie derivation, 2-local Lie derivation, Lie ring, Lie algebras, Lie ring of skew-adjoint matrices.
MSC: 17B40, 17B65, 46L57, 46L70, 46K70.
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