Left unital Kantor triple systems and structurable algebras
Alberto Elduque, Noriaki Kamiya, and Susumu Okubo
TL;DR
This paper establishes a correspondence between left unital Kantor triple systems and structurable algebras with involutive automorphisms, revealing new links to Lie superalgebras and their gradings.
Contribution
It introduces a novel correspondence between left unital Kantor triple systems and structurable algebras with involutions, expanding understanding of algebraic structures.
Findings
Left unital Kantor triple systems correspond to structurable algebras with involutive automorphisms.
A similar correspondence is shown for (-1,-1) Freudenthal-Kantor triple systems.
Connections to Lie superalgebras graded over root systems are established.
Abstract
Left unital Kantor triple systems will be shown to correspond to structurable algebras endowed with an involutive automorphism. A related result is proved for (-1,-1) Freudenthal-Kantor triple systems. Some consequences for the associated 5-graded Lie algebras and superalgebras are deduced too. In particular, left unital (-1,-1) Freudenthal-Kantor triple systems are shown to be intimately related to Lie superalgebras graded over the root system of type B(0,1).
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons