doi:10.1016/j.jpaa.2022.107277engAyupov, ShavkatElduque, AlbertoKudaybergenov, KarimbergenLocal derivations and automorphisms of Cayley algebrasART-2022-132353The present paper is devoted to the description of local and 2-local derivations and automorphisms on Cayley algebras over an arbitrary field F. Given a Cayley algebra C with norm n, let C0 be its subspace of trace 0 elements. We prove that the space of all local derivations of C coincides with the Lie algebra {d ∈ so(C, n) | d(1) = 0} which is isomorphic to the orthogonal Lie algebra so(C0, n). Surprisingly, the behavior of 2-local derivations depends on the Cayley algebra eing split or division. Every 2-local derivation on the split Cayley algebra is a derivation, so they are isomorphic to the exceptional Lie algebra g2(F) if charF = 2, 3. On the other hand, on division Cayley algebras over a field F, the sets of 2-local derivations and local derivations coincide. As a corollary we obtain descriptions of local and 2-local derivations of the seven-dimensional simple non-Lie Malcev algebras over fields of characteristic = 2, 3. Further, we prove that the group of all local automorphisms of C coincides with the group {φ ∈ O(C, n) | φ(1) = 1}. As in the case of 2-local derivations, the behavior of 2-local automorphisms depends on the Cayley algebra being split or division. Every 2-local automorphism on the split Cayley algebra is an automorphism, so they form the exceptional Lie group G2(F) if charF = 2, 3. On the other hand, on division Cayley algebras over a field F, the groups of 2-local automorphisms and local automorphisms coincide.2022http://zaguan.unizar.es/record/13016310.1016/j.jpaa.2022.107277http://zaguan.unizar.es/record/130163oai:zaguan.unizar.es:130163info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-83506-C2-1-Pinfo:eu-repo/grantAgreement/ES/DGA/E22-17Rinfo:eu-repo/grantAgreement/ES/DGA-FEDER/Construyendo Europa desde AragónJOURNAL OF PURE AND APPLIED ALGEBRA 227, 5 (2022), 107277 [16 pp.]by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/embargoedAccess