Cubist algebras

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...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2008-03, Vol.217 (4), p.1614-1670
Main Authors: Chuang, Joseph, Turner, Will
Format: Article
Language:English
Subjects:
Cubist
Tilings
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Summary: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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2007.06.017