Two geometric proofs of the classification of algebraic supergroups with semisimple representation theory

Abstract

We present two novel proofs of the known classification of connected affine algebraic supergroups $G$ such that $\mathrm{Rep}G$ is semisimple. The proofs are geometrically motivated, although both rely on an algebraic lemma that characterizes $\mathfrak{osp}(1|2n)$ amongst simple Lie superalgebras.

8 pages; minor typos fixed

References in corpus (1)

• Jacobson-Morozov Lemma for Algebraic Supergroups