Derivations of the Cheng-Kac Jordan superalgebras
Elisabete Barreiro, Alberto Elduque, and Consuelo Martinez
TL;DR
This paper investigates the derivations of Cheng-Kac Jordan superalgebras, showing their Lie superalgebra of derivations is isomorphic to a Tits-Kantor-Koecher construction from a simpler superalgebra, leveraging S4-symmetry.
Contribution
It establishes an isomorphism between the derivation Lie superalgebra of Cheng-Kac Jordan superalgebras and a Tits-Kantor-Koecher construction, revealing structural insights.
Findings
Derivations form a Lie superalgebra isomorphic to a Tits-Kantor-Koecher construction.
The S4-symmetry of the superalgebra is key to the derivation analysis.
Assuming -1 is a square in the ground field is crucial for the results.
Abstract
The derivations of the Cheng-Kac Jordan superalgebras are studied. It is shown that, assuming -1 is a square in the ground field, the Lie superalgebra of derivations of a Cheng-Kac Jordan superalgebra is isomorphic to the Lie superalgebra obtained from a simpler Jordan superalgebra (a Kantor double superalgebra of vector type) by means of the Tits-Kantor-Koecher construction. This is done by exploiting the S4-symmetry of the Cheng-Kac Jordan superalgebra.
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