A characterisation of indecomposable web-modules over Khovanov-Kuperberg Algebras

Abstract

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

References in corpus (1)

• A large family of indecomposable projective modules for the Khovanov-Kuperberg algebra of $s{l}_3$-webs

Cited by in corpus (6)

• The Blanchet-Khovanov algebras
• Integral presentations of quantum lattice Heisenberg algebras
• A closed formula for the evaluation of ${\mathfrak{sl}}_N$-foams
• ${\mathfrak{gl}}_n$-webs, categorification and Khovanov-Rozansky homologies
• Generic ${\mathfrak{gl}}_2$-foams, web and arc algebras
• Tensor diagrams and Chebyshev polynomials