Geodesic
A characterization of indecomposable web modules over Khovanov–Kuperberg algebras
Robert, Louis-Hadrien1
1MIN Fakultät, Fachbereich Mathematik, Bundesstraße 55, 20146 Hamburg, Germany
Algebraic and Geometric Topology, Tome 15 (2015) no. 3, pp. 1303-1362
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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.

DOI : 10.2140/agt.2015.15.1303
Classification : 17B37, 57M27, 57R56
Keywords: $\mathfrak{sl}_3$ homology, knot homology, categorification, webs and foams, $0+1+1$ TQFT

Robert, Louis-Hadrien  1

1 MIN Fakultät, Fachbereich Mathematik, Bundesstraße 55, 20146 Hamburg, Germany 
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Robert, Louis-Hadrien. A characterization of indecomposable web modules over Khovanov–Kuperberg algebras. Algebraic and Geometric Topology, Tome 15 (2015) no. 3, pp. 1303-1362. doi: 10.2140/agt.2015.15.1303

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