Compact Exceptional Simple Kantor Triple Systems Defined on Tensor Products of Composition Algebras∗

Mondoc, Daniel

doi:10.1080/00927870701404739

Cited by 13 publications

(6 citation statements)

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“…In this paper we continue the work on compact simple Kantor triple systems of [5] and [20,21,22] giving, by a unified formula (Theorem 1), the classification of exceptional compact simple Kantor triple systems defined on the realification of the 2 × 2-matrix algebra determined by Jordan algebra J = H 3 (A C ) of hermitian 3 × 3-matrices over a complex composition algebra A C corresponding to realifications of complex exceptional simple Lie algebras (Theorem 2). In addition, we give an explicit formula for the quadratic canonical trace form for these Kantor triple systems (Corollary 1).…”

Section: Introductionmentioning

confidence: 93%

On compact realifications of exceptional simple Kantor triple systems

Mondoc¹

2007

J Generalized Lie Theory Appl

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Let A be the realification of the matrix algebra determined by Jordan algebra of hermitian matrices of order three over a complex composition algebra. We define an involutive automorphism on A with a certain action on the triple system obtained from A which give models of simple compact Kantor triple systems. In addition, we give an explicit formula for the canonical trace form and the classification for these triples and their corresponding exceptional real simple Lie algebras. Moreover, we present all realifications of complex exceptional simple Lie algebras as Kantor algebras for a compact simple Kantor triple system defined on a structurable algebra of skew-dimension one.

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Section: Introductionmentioning

confidence: 93%

On compact realifications of exceptional simple Kantor triple systems

Mondoc¹

2007

J Generalized Lie Theory Appl

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“…Structurable algebras are a class of nonassociative algebras with involution that include Jordan algebras (with trivial involution), associative algebras with involution, and alternative algebras with involution. They are related to GJTSs of second order (or (−1, 1)-FKTSs) as introduced and studied in [31,32] and further studied in [3,4,30,[39][40][41][42]45] (see also references therein). Their importance lies with constructions of five graded Lie algebras…”

Section: δ-Structurable Algebrasmentioning

confidence: 99%

A Structure Theory of (−1,−1)-Freudenthal Kantor Triple Systems

Kamiya

Mondoc

Ôkubo

2009

Bull. Aust. Math. Soc.

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In this paper we discuss the simplicity criteria of (−1, −1)-Freudenthal Kantor triple systems and give examples of such triple systems, from which we can construct some Lie superalgebras. We also show that we can associate a Jordan triple system to any (ε, δ)-Freudenthal Kantor triple system. Further, we introduce the notion of δ-structurable algebras and connect them to (−1, δ)-Freudenthal Kantor triple systems and the corresponding Lie (super)algebra construction.2000 Mathematics subject classification: primary 17A40, 17B60.

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“…Structurable algebras are a class of nonassociative algebras with involution that include Jordan algebras (with trivial involution), associative algebras with involution, and alternative algebras with involution. They are related to GJTSs of 2nd order, or (−1, 1)-FKTSs, as introduced and studied in [20,21] and further studied in [3,4,19,26,27,28,29,30] (see also references therein). Their importance lies with constructions of 5-graded Lie algebras…”

Section: δ-Structurable Algebrasmentioning

confidence: 99%