Computing the group of minimal non-degenerate extensions of a super-Tannakian category

TL;DR

This paper studies the structure of minimal non-degenerate extensions of super-Tannakian categories, providing a K"unneth formula analog and explicit computations for specific cases.

Contribution

It introduces a K"unneth formula analog for minimal non-degenerate extensions and details the structure of these groups for pointed super-Tannakian categories.

Findings

Derived a K"unneth formula analog for extension groups

Described the structure of minimal extension groups resembling third cohomology

Computed the extension groups explicitly in several examples

Abstract

We prove an analog of the K\"unneth formula for the groups of minimal non-degenerate extensions arXiv:1602.05936 of symmetric fusion categories. We describe in detail the structure of the group of minimal extensions of a pointed super-Tannakian fusion category. This description resembles that of the third cohomology group of a finite abelian group. We explicitly compute this group in several concrete examples.