A characterization of indecomposable web modules over Khovanov–Kuperberg algebras
| Autor: | Louis-Hadrien Robert |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA) |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Categorification Geometric Topology (math.GT) Characterization (mathematics) 17B37 webs and foams Mathematics - Geometric Topology categorification $0+1+1$ TQFT 57M27 Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Geometry and Topology Representation Theory (math.RT) $\mathfrak{sl}_3$ homology 57R56 [MATH]Mathematics [math] Mathematics::Representation Theory Indecomposable module knot homology Mathematics - Representation Theory Mathematics |
| Zdroj: | Algebraic and Geometric Topology Algebraic and Geometric Topology, 2015, 15 (3), pp.1303-1362. ⟨10.2140/agt.2015.15.1303⟩ Algebr. Geom. Topol. 15, no. 3 (2015), 1303-1362 |
| ISSN: | 1472-2747 1472-2739 |
| DOI: | 10.2140/agt.2015.15.1303⟩ |
| Popis: | After shortly recalling the construction of the Khovanov-Kuperberg algebras, we give a characterisation of indecomposable web-modules. It says that a web-module is indecomposable if and only if one can deduce it directly from the Kuperberg bracket (via a Schur lemma argument). The proofs 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, for a web $w$ the Schur lemma does not apply, one can find an appropriate red graph for $w$. 46 pages, 53 figures, comments welcome |
| Databáze: | OpenAIRE |
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