Cartan matrices and presentations of the exceptional simple Elduque Lie superalgebra

2006/11/13 by Sofiane Bouarroudj, Bouarroudj, Sofiane, Pavel Grozman +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.RT #msc:17B50 #msc:70F25

paper · pdf · doi:10.48550/arxiv.math/0611392

5 pages, 1 figure, LaTeX2e

arxiv created 2006/11/13 · arxiv updated 2009/12/01

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.

Citations

• Some new simple modular Lie superalgebras

Cited by

• Semisimplifying Lie algebras of J-ternary algebras in characteristic 3

Related

• Cartan matrices and presentations of Cunha and Elduque superalgebras
• Models of some simple modular Lie superalgebras
• On reflections of roots in positive characteristic
• The five exceptional simple Lie superalgebras of vector fields
• On representations of Cartan map Lie superalgebras