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: Article (PostPrint)
Área (Departamento): Área Algebra (Dpto. Matemáticas)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material.
Fecha de embargo : 2025-05-31
Exportado de SIDERAL (2024-03-18-16:55:18)
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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: Article (PostPrint)
Área (Departamento): Área Algebra (Dpto. Matemáticas)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material. Fecha de embargo : 2025-05-31
Exportado de SIDERAL (2024-03-18-16:55:18)
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Record created 2024-01-23, last modified 2024-03-19