2003
DOI: 10.1081/agb-120023148
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Ternary Derivations of Generalized Cayley–Dickson Algebras

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Cited by 27 publications
(23 citation statements)
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“…The notion of a ternary derivation (in the algebra setting) was introduced by Jiménez-Gestal and Pérez-Izquierdo [19]. The concept of a ternary derivation goes back to the so-called triality principle, which states that every element of the orthogonal Lie algebra of skew-symmetric operators of the Cayley-Dickson algebra under the composition form is the principal component of a ternary derivation.…”
Section: Ternary Derivationsmentioning
confidence: 99%
“…The notion of a ternary derivation (in the algebra setting) was introduced by Jiménez-Gestal and Pérez-Izquierdo [19]. The concept of a ternary derivation goes back to the so-called triality principle, which states that every element of the orthogonal Lie algebra of skew-symmetric operators of the Cayley-Dickson algebra under the composition form is the principal component of a ternary derivation.…”
Section: Ternary Derivationsmentioning
confidence: 99%
“…The definition of a ternary derivation arised in the paper of Perez-Izquierdo and JimenezGestal [2]. A ternary derivation is a triple of linear mappings (D, F, G) such that D(xy) = F (x)y + xG(y).…”
Section: Corollarymentioning
confidence: 99%
“…Квазидифференцирова-ния, обобщенные дифференцирования и тернарные дифференцирования рассматри-вались в работах [17]- [26]. В частности, изучались обобщенные и тернарные диффе-ренцирования алгебр Ли [17], супералгебр Ли [18], ассоциативных алгебр [19], [20], обобщенных алгебр Кэли-Диксона [21], йордановых алгебр и супералгебр [24], [25] и алгебр Мальцева [26]. Необходимо отметить, что в предшествующих работах (см.…”
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