Almost-simple algebraic supergroups

2025/11/20 by Bouarroudj, S., Zubkov, A. N.
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Finite Group Theory Research

paper · doi:10.48550/arxiv.2511.16293

Abstract

We describe certain almost-simple algebraic supergroups over an algebraically closed field of odd or zero characteristic. In addition to supergroups with simple Lie superalgebras from Kac's theorem, we construct new supergroups whose Lie superalgebra is either non-simple or simple but is not part of Kac's list.

Citations

• Orbits of actions of group superschemes
• Group superschemes
• Invariants of G₂ and Spin(7) in positive characteristic
• On functor points of affine supergroups
• Solvability and nilpotency for algebraic supergroups
• Solvable, reductive and quasireductive supergroups
• Some Good-Filtration Subgroups of Simple Algebraic Groups
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• An extended Freudenthal Magic Square in characteristic 3

Related

• The minimal number of generators for simple Lie superalgebras
• Generators of simple Lie superalgebras in characteristic 0
• Two geometric proofs of the classification of algebraic supergroups with\n semisimple representation theory
• Quotients of complex algebraic supergroups
• Group gradings on classical Lie superalgebras