Cartan matrices and presentations of the exceptional simple Elduque Lie superalgebra

Sofiane Bouarroudj, Pavel Grozman, and Dimitry A. Leites

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Submission date: 09. Nov. 2006
Pages: 7
Bibtex
MSC-Numbers: 17B5, 70F25
Keywords and phrases: Elduque superalgebra, Lie superalgebra, Cartan matrix
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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.