Grothendieck groups of the Khovanov-Kuperberg algebras

Abstract

The aim of this note is to take benefit of the foam nature of the Khovanov-Kuperberg algebras to compute the Grothendieck groups of their categories of finitely generated projective modules. The computation relies on the Hattori-Stallings trace and some geometrical properties of foams in a solid torus.

arXiv comment19 pages, 16 figures, comments welcome. arXiv admin note: text overlap with arXiv:1309.2793