On certain integral tensor categories and integral TQFTs

TL;DR

This paper constructs tensor categories with finitely many simple objects over rings of algebra integers and demonstrates how to derive topological quantum field theories (TQFTs) over algebra integers from these categories.

Contribution

It introduces a new class of tensor categories over algebra integers and provides a method to obtain integral TQFTs from them.

Findings

Tensor categories dominated by finitely many simple objects.

Construction of TQFTs over algebra integers.

Framework for modules over rings of algebra integers.

Abstract

We construct certain tensor categories that are dominated by finitely many simple objects. Objects in these categories are modules over rings of algebra integers. We show how to obtain TQFTs defined over algebra integers from these categories.