A non-semisimple Witt class

TL;DR

This paper introduces new examples of braided finite tensor categories, including a non-degenerate one that is not Witt equivalent to any semisimple category, expanding the understanding of tensor category classifications.

Contribution

It presents several infinite families of braided finite tensor categories, notably a non-semisimple example that challenges existing Witt classification assumptions.

Findings

Identified infinite families of braided finite tensor categories.

Constructed a non-degenerate braided tensor category not Witt equivalent to semisimple categories.

Provided insights into the structure of non-semisimple tensor categories.

Abstract

We describe several infinite families of braided finite tensor categories. A simplest example gives a non-degenerate braided tensor category which is not Witt equivalent to a semisimple category.