Cartan matrices and presentations of Cunha and Elduque superalgebras

TL;DR

This paper classifies all inequivalent Cartan matrices and provides defining relations for the simple roots of ten exceptional finite-dimensional Lie superalgebras in characteristic 3, expanding understanding of their structure.

Contribution

It enumerates all inequivalent Cartan matrices and presents defining relations for these superalgebras, a novel comprehensive classification in characteristic 3.

Findings

List of all inequivalent Cartan matrices for the superalgebras.

Explicit defining relations between Chevalley generator analogs.

Enhanced structural understanding of these superalgebras in characteristic 3.

Abstract

All inequivalent Cartan matrices (in other words, inequivalent systems of simple roots) of the ten simple exceptional finite dimensional Lie superalgebras in characteristic 3, recently identified by Cunha and Elduque as constituents of Elduque's superization of the Freudenthal Magic Square, are listed together with defining relations between analogs of their Chevalley generators.