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Positivstellensatz for C*-tensor categories

Kajal Das, Mainak Ghosh, Shamindra Ghosh

Abstract

We explore semi-pre-C*-algebras in the context of rigid semisimple C*-tensor categories and using techniques from annular representations, we extend Ozawa's criterion for property (T) in groups to this context

Positivstellensatz for C*-tensor categories

Abstract

We explore semi-pre-C*-algebras in the context of rigid semisimple C*-tensor categories and using techniques from annular representations, we extend Ozawa's criterion for property (T) in groups to this context

Paper Structure

This paper contains 6 sections, 12 theorems, 21 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Rigid C*-tensor categories
  4. Tube algebras
  5. Semi-pre-C*-algebras
  6. Main theorem

Key Result

Theorem 1.1

The fusion algebra is a semi-pre-C*-algebra with respect to the tube cone

Theorems & Definitions (35)

  • Theorem 1.1
  • Proposition 1.2
  • Theorem 1.3
  • Remark 2.1
  • Remark 2.2
  • Definition 2.3
  • Remark 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.7
  • ...and 25 more