Cubist Algebras
Representation Theory
2007-10-30 v1 Combinatorics
Abstract
We construct algebras from rhombohedral tilings of Euclidean space obtained as projections of certain 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 weight 2 blocks of symmetric groups.
Cite
@article{arxiv.0710.5457,
title = {Cubist Algebras},
author = {J. Chuang and W. Turner},
journal= {arXiv preprint arXiv:0710.5457},
year = {2007}
}