Title: The Grothendieck groups of Khovanov-Kuperberg Algebras
2013.11.26 |
| Date | Wed 05 Feb |
| Time | 15:15 — 16:15 |
| Location | Aud. D3 |
Abstract:
The $sl3$ homology is a variant of the Khovanov homology. The construction starts with $sl3$ instead of $sl2$. The TQFT counterpart of the $sl3$ homology involves foams rather than surfaces. The Khovanov homology and the $sl3$ homology have a version for tangles. It involves some algebras called $Hn$ in the first case and $K?$ in the second. The projective indecomposable modules over these algebras decategorify on dual canonical bases. While in the $sl2$ case this modules are very easy to identity, but in the $sl3$ case this is much more difficult. In this talk, after setting the framework, I will explain why the $sl3$ is, indeed, more complicated and show that there are natural bases for the Grothendieck groups of the algebras $K?$. This result was previously proven by Mackaay-Pan-Tubbenhauer, but the approach I will explain is new and completely topological.
