Cartan matrices and presentations of the exceptional simple Elduque Lie superalgebra

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.