Volume 15, issue 3 (2015)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A characterization of indecomposable web modules over Khovanov–Kuperberg algebras

Louis-Hadrien Robert

Algebraic & Geometric Topology 15 (2015) 1303–1362
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.

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