On compact realifications of exceptional simple Kantor triple systems

Mondoc, Daniel

doi:10.4303/jglta/s060103

Cited by 8 publications

(2 citation statements)

References 10 publications

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“…The second identity in (3.40), that is x = x, follows from Lemma 3.1, that is from the identity R 2 (x) = x since we have shown above that R(x) = x; hence R 2 (x) = x. 44) where x := (xee) and x · y is the bilinear product of U defined by (3.27).…”

Section: (Exe) = Rq(x) − Qr(x) + (Exe) That Is Rq(x) = Qr(x)mentioning

confidence: 99%

A Characterization of (−1, −1)-Freudenthal–kantor Triple Systems

2011

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Abstract. In this paper, we discuss a connection between (−1, −1)-FreudenthalKantor triple systems, anti-structurable algebras, quasi anti-flexible algebras and give examples of such structures. The paper provides the correspondence and characterization of a bilinear product corresponding a triple product. associated with an (ε, δ)-Freudenthal-Kantor triple system. In particular, we deal with a characterization of triple systems from the point of view of a bilinear product by means of anti-structurable algebras or balanced property. Specially, Jordan and Lie (super)algebras [9, 13, 52] play an important role in many mathematical and physical subjects [ 5, 11-14, 16, 26, 29, 37, 47, 48, 55, 56]). We also note that the construction and characterization of these algebras can be expressed in terms of triple systems [20, 23,24,28,38,49] by using the standard embedding method [22,41,42,50,54].

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Section: (Exe) = Rq(x) − Qr(x) + (Exe) That Is Rq(x) = Qr(x)mentioning

confidence: 99%

A Characterization of (−1, −1)-Freudenthal–kantor Triple Systems

2011

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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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On Certain Algebraic Structures Associated with Lie (Super)Algebras

Kamiya

2023

Springer Proceedings in Mathematics &Amp; Statistics

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On compact realifications of exceptional simple Kantor triple systems

Cited by 8 publications

References 10 publications

A Characterization of (−1, −1)-Freudenthal–kantor Triple Systems

A Characterization of (−1, −1)-Freudenthal–kantor Triple Systems

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

On Certain Algebraic Structures Associated with Lie (Super)Algebras

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