Cubist algebras.

Joseph Chuang and Will Turner

Abstract:
We construct algebras from rhombohedral tilinigs of Euclidean space 
obtained as projections of cubical complexes. We show that these "Cubist 
algebras" satisfy strong homological properties, such as Koszulity and 
quasi-heredity, reflecting the combinatorics of the tilings. We construct 
derived equivalences between Cubist algebras associated to local mutations 
in tilings. We recover as a special case the Rhombal algebras of Michael 
Peach, and make a precise connection to symmetric group blocks of weight 
two.