The Supermagic Square in characteristic 3 and Jordan superalgebras
Isabel Cunha (Universidade da Beira Interior), Alberto Elduque, (Universidad de Zaragoza)
TL;DR
This paper reviews the extension of the Freudenthal Magic Square over fields of characteristic 3, highlighting new Lie superalgebras and their isomorphisms with Tits-Kantor-Koecher Lie superalgebras of Jordan superalgebras.
Contribution
It introduces the Supermagic Square in characteristic 3 and demonstrates isomorphisms between certain Lie superalgebras and Jordan superalgebras.
Findings
Extension of the Magic Square in characteristic 3
Identification of new simple Lie superalgebras
Isomorphisms with Tits-Kantor-Koecher Lie superalgebras
Abstract
Recently, the classical Freudenthal Magic Square has been extended over fields of characteristic 3 with two more rows and columns filled with (mostly simple) Lie superalgebras specific of this characteristic. This Supermagic Square will be reviewed and some of the simple Lie superalgebras that appear will be shown to be isomorphic to the Tits-Kantor-Koecher Lie superalgebras of some Jordan superalgebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras · Fuzzy and Soft Set Theory