On rank one 2-representations of web categories

Tubbenhauer, Daniel

doi:10.5802/alco.389

Tubbenhauer, Daniel ¹

¹ The University of Sydney School of Mathematics and Statistics F07, Office Carslaw 827 NSW 2006, Australia

Algebraic Combinatorics, Volume 7 (2024) no. 6, pp. 1813-1843.

Abstract

We classify rank one 2-representations of ${SL}_{2}$ , ${GL}_{2}$ and ${SO}_{3}$ 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.

Received: 2023-10-02
Revised: 2024-06-16
Accepted: 2024-07-06
Published online: 2025-01-07

Zbl

DOI: 10.5802/alco.389

Classification: 18M05, 18M30, 22E46, 22E47
Mots-clés : Webs, 2-representations, bilinear and trilinear forms

Author's affiliations:

Tubbenhauer, Daniel ¹

¹ The University of Sydney School of Mathematics and Statistics F07, Office Carslaw 827 NSW 2006, Australia

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Tubbenhauer, Daniel. On rank one 2-representations of web categories. Algebraic Combinatorics, Volume 7 (2024) no. 6, pp. 1813-1843. doi : 10.5802/alco.389. https://alco.centre-mersenne.org/articles/10.5802/alco.389/

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