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Description of 2-local derivations and automorphisms on finite dimensional Jordan algebras (1911.03194v2)
Published 8 Nov 2019 in math.RA and math.OA
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.