Almost-simple algebraic supergroups

TL;DR

This paper classifies and constructs various almost-simple algebraic supergroups over algebraically closed fields, including new examples with non-simple or non-listed simple Lie superalgebras, expanding the understanding of supergroup structures.

Contribution

It introduces new supergroups with Lie superalgebras outside Kac's classification, broadening the landscape of algebraic supergroup theory.

Findings

Classification of almost-simple algebraic supergroups over algebraically closed fields.

Construction of new supergroups with non-simple or non-listed simple Lie superalgebras.

Extension of known supergroup structures beyond Kac's theorem.

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.