000130163 001__ 130163
000130163 005__ 20240319081028.0
000130163 0247_ $$2doi$$a10.1016/j.jpaa.2022.107277
000130163 0248_ $$2sideral$$a132353
000130163 037__ $$aART-2022-132353
000130163 041__ $$aeng
000130163 100__ $$aAyupov, Shavkat
000130163 245__ $$aLocal derivations and automorphisms of Cayley algebras
000130163 260__ $$c2022
000130163 5060_ $$aAccess copy available to the general public$$fUnrestricted
000130163 5203_ $$aThe 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.
000130163 536__ $$9info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-83506-C2-1-P$$9info:eu-repo/grantAgreement/ES/DGA/E22-17R$$9info:eu-repo/grantAgreement/ES/DGA-FEDER/Construyendo Europa desde Aragón
000130163 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000130163 590__ $$a0.8$$b2022
000130163 591__ $$aMATHEMATICS$$b170 / 329 = 0.517$$c2022$$dQ3$$eT2
000130163 591__ $$aMATHEMATICS, APPLIED$$b210 / 267 = 0.787$$c2022$$dQ4$$eT3
000130163 592__ $$a0.887$$b2022
000130163 593__ $$aAlgebra and Number Theory$$c2022$$dQ1
000130163 594__ $$a1.6$$b2022
000130163 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000130163 700__ $$0(orcid)0000-0002-6497-2162$$aElduque, Alberto$$uUniversidad de Zaragoza
000130163 700__ $$aKudaybergenov, Karimbergen
000130163 7102_ $$12006$$2005$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Algebra
000130163 773__ $$g227, 5 (2022), 107277 [16 pp.]$$pJ. pure appl. algebra$$tJOURNAL OF PURE AND APPLIED ALGEBRA$$x0022-4049
000130163 8564_ $$s370360$$uhttps://zaguan.unizar.es/record/130163/files/texto_completo.pdf$$yPostprint$$zinfo:eu-repo/date/embargoEnd/2025-05-31
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000130163 909CO $$ooai:zaguan.unizar.es:130163$$particulos$$pdriver
000130163 951__ $$a2024-03-18-16:55:18
000130163 980__ $$aARTICLE