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arXiv · 2204.03234

Local and 2-local derivations on Lie matrix rings over commutative involutive rings

Shavkat Ayupov·Farhodjon Arzikulov·Sardorbek Umrzaqov
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Abstract

In the present paper 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 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. We also show that every local spatial derivation on the above Lie algebras is a derivation.

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Shavkat Ayupov, Farhodjon Arzikulov, Sardorbek Umrzaqov. 2022-04-07. Local and 2-local derivations on Lie matrix rings over commutative involutive rings. https://arxiv.org/abs/2204.03234

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