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On rank one 2-representations of web categories

Daniel Tubbenhauer

TL;DR

Rank one 2-representations of SL2, GL2 and SO3 web categories are classified by reducing the problem to the classification of bilinear and trilinear forms, and is formulated such that it can be adapted to other web categories.

Abstract

We classify rank one 2-representations of SL2, GL2 and SO3 web categories. The classification is inspired by similar results about quantum groups, given by reducing the problem to the classification of bilinear and trilinear forms, and is formulated such that it can be adapted to other web categories.

On rank one 2-representations of web categories

TL;DR

Rank one 2-representations of SL2, GL2 and SO3 web categories are classified by reducing the problem to the classification of bilinear and trilinear forms, and is formulated such that it can be adapted to other web categories.

Abstract

We classify rank one 2-representations of SL2, GL2 and SO3 web categories. The classification is inspired by similar results about quantum groups, given by reducing the problem to the classification of bilinear and trilinear forms, and is formulated such that it can be adapted to other web categories.
Paper Structure (18 sections, 52 theorems, 51 equations)

This paper contains 18 sections, 52 theorems, 51 equations.

Table of Contents

  1. Introduction
  2. Motivation and results
  3. A few extra comments
  4. Background on 2-representations
  5. Rank one 2-representations of SL2 webs
  6. SL2 webs
  7. The main theorem in the SL2 case
  8. Proof of \ref{['T:RepsSL2Main']}
  9. Proof of \ref{['P:RepsSL2Main']}
  10. Rank one 2-representations of GL2 webs
  11. GL2 webs
  12. The main theorem in the GL2 case
  13. Proof of \ref{['T:RepsGL2Main']}
  14. Rank one 2-representations of SO3 webs
  15. SO3 webs
  16. ...and 3 more sections

Key Result

Lemma 1

We have:

Theorems & Definitions (148)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Definition 1
  • Lemma 1
  • proof
  • Remark 6
  • Definition 2
  • ...and 138 more