A characterization of indecomposable web modules over Khovanov–Kuperberg algebras

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.

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Keywords

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

Mathematical Subject Classification 2010

Primary: 17B37

Secondary: 57M27, 57R56

References

Publication

Received: 13 September 2013

Revised: 8 August 2014

Accepted: 27 August 2014

Published: 19 June 2015

Authors

Louis-Hadrien Robert
MIN Fakultät Fachbereich Mathematik Bundesstraße 55 20146 Hamburg Germany
http://www.math.uni-hamburg.de/home/robert/index.html

Volume 15, issue 3 (2015)

Louis-Hadrien Robert

Abstract