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The Grothendieck groups of Khovanov-Kuperberg Algebras

Louis-Hadrien Robert
(IRMA Strasbourg)
Seminar
Onsdag, 5 februar, 2014, at 15:15-16:15, in Aud. D3 (1531-215)
Abstrakt:
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 Kǫ 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 Kǫ. This result was previously proven by Mackaay-Pan-Tubbenhauer, but the approach I will explain is new and completely topological.
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen