Description of 2-local and local derivations on some Lie rings of skew-adjoint matrices
Sh. A. AyupovV. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, UzbekistanFarhodjon ArzikulovDepartment of Mathematics, Andizhan State University, Andizhan, Uzbekistan
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Annotatsiya
In the present paper, we prove that every 2-local inner derivation on the Lie ring of skew-symmetric matrices over a commutative ring is an inner derivation. We also apply our technique to various Lie algebras of infinite-dimensional skew-adjoint matrix-valued maps on a set and prove that every 2-local spatial derivation on such algebras is a spatial derivation. A similar technique is applied to the same Lie algebras and proved that every local spatial derivation on such algebras is a spatial derivation.
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