Cartan matrices and presentations of the exceptional simple Elduque Lie superalgebra
Sofiane Bouarroudj, Pavel Grozman, Dimitry Leites

TL;DR
This paper explores the structure of an exceptional Lie superalgebra in characteristic 5, detailing its Cartan matrices and defining relations, thus advancing understanding of its algebraic presentation.
Contribution
It provides a complete list of inequivalent Cartan matrices and defining relations for the exceptional Elduque Lie superalgebra in characteristic 5.
Findings
Classified all inequivalent Cartan matrices for the superalgebra
Presented defining relations between Chevalley generators
Identified the superalgebra as exceptional in characteristic 5
Abstract
Recently Alberto Elduque listed all simple and graded modulo 2 finite dimensional Lie algebras and superalgebras whose odd component is the spinor representation of the orthogonal Lie algebra equal to the even component, and discovered one exceptional such Lie superalgebra in characteristic 5. For this Lie superalgebra all inequivalent Cartan matrices (in other words, inequivalent systems of simple roots) are listed together with defining relations between analogs of its Chevalley generators.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons
