Description of 2-local derivations on some Lie rings of skew-adjoint matrices

2018/03/16 by Ayupov, Shavkat, Arzikulov, Farhodjon
#16W25 #17B40 #17B65 #46L57 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1803.06281

Abstract

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.

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• Local and 2-local derivations on Lie matrix rings over commutative involutive rings
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• 2-Local derivations on matrix rings over associative rings
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• Local derivations on associative and Jordan matrix algebras