The Cayley–Dickson process for dialgebras

DOI10.1080/03081087.2013.791817zbMath1378.17005arXiv1209.2645OpenAlexW2162800606MaRDI QIDQ5495759

Raúl Felipe, Raúl Felipe-Sosa, Juana Sánchez-Ortega, Murray R. Bremner, Michael K. Kinyon

Publication date: 7 August 2014

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.2645

zbMATH Keywords

Leibniz algebrasCayley-Dickson processJordan dialgebrasKP algorithmdialgebras with involution

Mathematics Subject Classification ID

Jordan structures associated with other structures (17C50) Leibniz algebras (17A32) Alternative rings (17D05) Composition algebras (17A75) Nonassociative algebras satisfying other identities (17A30) Mal'tsev rings and algebras (17D10) Flexible algebras (17A20)

Related Items (3)

Ω-Algebras with split products ⋮ On the definitions of nucleus for dialgebras ⋮ On the Cayley-Dickson process for dialgebras

Cites Work

• Jordan triple disystems
• Some results on L-dendriform algebras
• Hopf algebra of the planar binary trees
• Universal enveloping algebras of Leibniz algebras and (co)homology
• J-dendriform algebras
• Steinberg-Leibniz algebras and superalgebras
• Quasialgebra structure of the octonions
• Quadri-algebras
• Embedding of dendriform algebras into Rota-Baxter algebras
• Quadratic forms permitting composition
• On the Definition of Quasi-Jordan Algebra
• The Tits–Kantor–Koecher Construction for Jordan Dialgebras
• Malcev dialgebras
• Quasi-Jordan Algebras
• Manin products, Koszul duality, Loday algebras and Deligne conjecture
• Leibniz Algebras Graded by Finite Root Systems
• The octonions
• Un Theoreme de Poincaré–Birkhoff–Witt pour les Algebres de Leibniz
• On special identities for dialgebras

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