Algebraic & Geometric Topology

A characterization of indecomposable web modules over Khovanov–Kuperberg algebras

Louis-Hadrien Robert

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510840962

Digital Object Identifier
doi:10.2140/agt.2015.15.1303

Mathematical Reviews number (MathSciNet)
MR3361138

Zentralblatt MATH identifier
06451709

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.agt/1510840962


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