Local derivations and automorphisms of Cayley algebras

Ayupov, Shavkat ; Elduque, Alberto (Universidad de Zaragoza) ; Kudaybergenov, Karimbergen

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.jpaa.2022.107277

Año: 2022

Publicado en: JOURNAL OF PURE AND APPLIED ALGEBRA 227, 5 (2022), 107277 [16 pp.]
ISSN: 0022-4049

Factor impacto JCR: 0.8 (2022)

Categ. JCR: MATHEMATICS rank: 170 / 329 = 0.517 (2022) - Q3 - T2
Categ. JCR: MATHEMATICS, APPLIED rank: 210 / 267 = 0.787 (2022) - Q4 - T3

Factor impacto CITESCORE: 1.6 - Mathematics (Q3)

Factor impacto SCIMAGO: 0.887 - Algebra and Number Theory (Q1)

Financiación: info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-83506-C2-1-P
Financiación: info:eu-repo/grantAgreement/ES/DGA/E22-17R
Financiación: info:eu-repo/grantAgreement/ES/DGA-FEDER/Construyendo Europa desde Aragón

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Algebra (Dpto. Matemáticas)