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

TL;DR

This paper provides two new geometric proofs for classifying certain algebraic supergroups with semisimple representation theory, relying on an algebraic lemma related to Lie superalgebras.

Contribution

It introduces two novel geometric proofs for the classification of algebraic supergroups with semisimple representations, expanding understanding of their structure.

Findings

Classification of algebraic supergroups with semisimple representations confirmed

Two geometric proofs established for the classification

Key algebraic lemma characterizing rak{osp}(1|2n) among Lie superalgebras

Abstract

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