Elementary groups and invertibility for kantor pairs

DOI10.1080/00927879908826447zbMath0926.17019OpenAlexW2056436570MaRDI QIDQ4237101

John R. Faulkner, Bruce N. Allison

Publication date: 29 November 1999

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879908826447

zbMATH Keywords

invertibilityJordan pairtriple systemstructurable algebraelementary groupKantor pairEichler transformation

Mathematics Subject Classification ID

Structure theory for Jordan algebras (17C10) Associated groups, automorphisms of Jordan algebras (17C30)

Related Items

Extremal elements in Lie algebras, buildings and structurable algebras ⋮ On the Faulkner construction for generalized Jordan superpairs ⋮ Compact realifications of exceptional simple Kantor triple systems defined on tensor products of composition algebras ⋮ Simple associative algebras with finite \(\mathbb{Z}\)-grading ⋮ The Peirce decomposition for generalized Jordan triple systems of finite order ⋮ Quotients in graded Lie algebras. Martindale-like quotients for Kantor pairs and Lie triple systems ⋮ Moufang Sets and Structurable Division Algebras ⋮ Fine gradings on Kantor systems of Hurwitz type ⋮ Jordan Structures and Non-Associative Geometry ⋮ Compact Exceptional Simple Kantor Triple Systems Defined on Tensor Products of Composition Algebras∗ ⋮ STRUCTURABLE ALGEBRAS AND MODELS OF COMPACT SIMPLE KANTOR TRIPLE SYSTEMS DEFINED ON TENSOR PRODUCTS OF COMPOSITION ALGEBRAS ⋮ A Peirce Decomposition for Generalized Jordan Triple Systems of Second Order ⋮ Elementary subgroups of isotropic reductive groups ⋮ Dynkin diagrams and short Peirce gradings of Kantor pairs ⋮ Generalized conformal realizations of Kac–Moody algebras ⋮ 5-graded simple Lie algebras, structurable algebras, and Kantor pairs ⋮ Gradings on tensor products of composition algebras and on the Smirnov algebra ⋮ Models of Compact Simple Kantor Triple Systems Defined on a Class of Structurable Algebras of Skew-Dimension One ⋮ A realization of the Lie algebra associated to a Kantor triple system

Cites Work

• Isotopes of some nonassociative algebras with involution
• A class of nonassociative algebras with involution containing the class of Jordan algebras
• Elementary groups and stability for Jordan pairs
• Structurable triples, Lie triples, and symmetric spaces
• Higher order invertibility in jordan pairs