Cartan matrices and presentations of Cunha and Elduque superalgebras
Sofiane Bouarroudj, Pavel Grozman, Dimitry Leites

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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons
