A non-semisimple Witt class
Victor Ostrik, Alexandra Utiralova

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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology
