Ternary Derivations of Generalized Cayley–Dickson Algebras

Abstract

Ternary derivations, ternary Cayley derivations and ternary automorphisms are computed over fields of characteristic ≠ 2, 3 for the algebras A t obtained by the Cayley–Dickson duplication process. While the derivation algebra of A t stops growing after t = 3, the ternary derivation algebra significantly decreases in the step from the octonions A 3 to the sedenions A 4, revealing the symmetry lost on that stage.