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arXiv · 1911.03194

Description of 2-local derivations and automorphisms on finite dimensional Jordan algebras

Shavkat Ayupov·Farhodjon Arzikulov·Nodirbek Umrzaqov·Olimjon Nuriddinov
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Abstract

In the present paper we introduce and investigate the notion of 2-local linear map on vector spaces. A sufficient condition is obtained for linearity of a 2-local linear map on finite dimensional vector spaces. Based on this result we prove that every 2-local derivation on a finite dimensional formally real Jordan algebra is a derivation. Also we show that every 2-local 1-automorphism (i.e. implemented by single symmetries) of mentioned Jordan algebras is an automorphism.

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Shavkat Ayupov, Farhodjon Arzikulov, Nodirbek Umrzaqov, Olimjon Nuriddinov. 2019-11-08. Description of 2-local derivations and automorphisms on finite dimensional Jordan algebras. https://arxiv.org/abs/1911.03194

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