Algebraic & Geometric Topology

A characterization of indecomposable web modules over Khovanov–Kuperberg algebras

Louis-Hadrien Robert

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After shortly reviewing the construction of the Khovanov–Kuperberg algebras, we give a characterization of indecomposable web modules. It says that a web module is indecomposable if and only if one can deduce its indecomposability directly from the Kuperberg bracket (via a Schur lemma argument). The proof relies on the construction of idempotents given by explicit foams. These foams are encoded by combinatorial data called red graphs. The key point is to show that when the Schur lemma does not apply for a web w, an appropriate red graph for w can be found.

Article information

Algebr. Geom. Topol., Volume 15, Number 3 (2015), 1303-1362.

Received: 13 September 2013
Revised: 8 August 2014
Accepted: 27 August 2014
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
Secondary: 57M27: Invariants of knots and 3-manifolds 57R56: Topological quantum field theories

$\mathfrak{sl}_3$ homology knot homology categorification webs and foams $0+1+1$ TQFT


Robert, Louis-Hadrien. A characterization of indecomposable web modules over Khovanov–Kuperberg algebras. Algebr. Geom. Topol. 15 (2015), no. 3, 1303--1362. doi:10.2140/agt.2015.15.1303.

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