Local and 2-local derivations of the octonion algebra
F.N. Arzikulov, I.A. Karimjanov, S. Uguz
TL;DR
This paper investigates local and 2-local derivations in the octonion algebra, proving conditions under which they are derivations or Jordan derivations, thus advancing understanding of algebraic structures over octonions.
Contribution
It establishes that local derivations satisfying certain conditions are derivations, and all 2-local derivations are Jordan derivations in octonion algebra.
Findings
Local derivations under certain conditions are derivations
Every 2-local derivation is a Jordan derivation
Results hold over arbitrary fields
Abstract
In the present paper, we prove that a local derivation on the octonion (Cayley) algebra over an arbitrary field, satisfying some conditions is a derivation, and every 2-local derivation on is a Jordan derivation.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology