On reflections of roots in positive characteristic

2023/11/05 by Alexey Lebedev, Lebedev, Alexey
Computer Science · Mathematics · Physics and Astronomy · #17B50 (Primary) #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2311.02710

openalex publication_date 2023/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a Lie superalgebra with Cartan matrix over a field of positive characteristic, some information about its root system in terms of the system of simple roots corresponding to the Chevalley generators is described, under certain given assumptions. This information may be useful for finding other systems of simple roots of such a Lie superalgebra and other Cartan matrices which produce Lie superalgebras isomorphic to a given one.

Related

• Cartan matrices and presentations of the exceptional simple Elduque Lie superalgebra
• Cartan matrices and presentations of Cunha and Elduque superalgebras
• The invariant polynomials on simple Lie superalgebras
• Lie Superalgebras Graded by the Root System A(m,n)
• Chevalley Supergroups of type D(2,1;a)