A Cayley-Dickson Process for a Class of Structurable Algebras

DOI10.2307/1999997zbMath0543.17015OpenAlexW4230289672MaRDI QIDQ3331383

John R. Faulkner, Bruce N. Allison

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/1999997

zbMATH Keywords

involutionFreudenthal triple systemsCayley-Dickson processLie algebra constructionsreduced structurable algebrasseparable Jordan algebrasimple structurable algebrastructurable division algebras

Mathematics Subject Classification ID

Structure theory for nonassociative algebras (17A60) Simple, semisimple Jordan algebras (17C20) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60) Nonassociative algebras satisfying other identities (17A30)

Related Items

Extremal elements in Lie algebras, buildings and structurable algebras, Cubic Action of a Rank one Group, A survey on Albert algebras, Relaxed linear spaces and a generalization of the Cayley-Dickson process, Classes of structurable algebras of skew-rank, Round forms of higher degree, Construction process for simple Lie algebras, Automorphisms, derivations and gradings of the split quartic Cayley algebra, Moufang Sets and Structurable Division Algebras, Construction of \(3 \times{} 3\)-matrix Lie algebras and some Lie algebras of type \(D_ 4\), Fine gradings on Kantor systems of Hurwitz type, Structurable algebras of skew-dimension one and hermitian cubic norm structures, Structurable \(H^*\)-algebras, Minuscule embeddings, A rational construction of Lie algebras of type \(E_{7}\), Finding Octonion Algebras in Associative Algebras, Irreducible Lie-Yamaguti algebras, Isotropic trialitarian algebraic groups, Gradings on tensor products of composition algebras and on the Smirnov algebra, On structurable algebras

Cites Work

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• A class of nonassociative algebras with involution containing the class of Jordan algebras
• Norms and noncommutative Jordan algebras
• A proof of Schafer's conjecture for infinite-dimensional forms admitting composition
• Models of isotropic simple lie algebras
• A NEW TYPE OF NON ASSOCIATIVE ALGEBRAS
• Groups of type E7.
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