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

DOI10.1080/03081087.2020.1845595zbMATH Open1516.17027arXiv1911.03194MaRDI QIDQ6328772

Farkhad Nematjonovich Arzikulov, [[Person:6115382|Author name not available (Why is that?)]], Sh. A. Ayupov, N. M. Umrzaqov

Publication date: 8 November 2019

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.

Mathematics Subject Classification ID

Jordan structures associated with other structures (17C50) Jordan structures on Banach spaces and algebras (17C65) Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46Lxx)

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