130163 20240319081028.0 doi 10.1016/j.jpaa.2022.107277 sideral 132353 ART-2022-132353 eng Ayupov, Shavkat Local derivations and automorphisms of Cayley algebras 2022 Access copy available to the general public Unrestricted The 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. info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-83506-C2-1-P info:eu-repo/grantAgreement/ES/DGA/E22-17R info:eu-repo/grantAgreement/ES/DGA-FEDER/Construyendo Europa desde Aragón info:eu-repo/semantics/embargoedAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 0.8 2022 MATHEMATICS 170 / 329 = 0.517 2022 Q3 T2 MATHEMATICS, APPLIED 210 / 267 = 0.787 2022 Q4 T3 0.887 2022 Algebra and Number Theory 2022 Q1 1.6 2022 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Elduque, Alberto Universidad de Zaragoza (orcid)0000-0002-6497-2162 Kudaybergenov, Karimbergen 2006 005 Universidad de Zaragoza Dpto. Matemáticas Área Algebra 227, 5 (2022), 107277 [16 pp.] J. pure appl. algebra JOURNAL OF PURE AND APPLIED ALGEBRA 0022-4049 370360 http://zaguan.unizar.es/record/130163/files/texto_completo.pdf Postprint info:eu-repo/date/embargoEnd/2025-05-31 1748428 http://zaguan.unizar.es/record/130163/files/texto_completo.jpg?subformat=icon icon Postprint info:eu-repo/date/embargoEnd/2025-05-31 oai:zaguan.unizar.es:130163 articulos driver 2024-03-18-16:55:18 ARTICLE