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Cubist algebras

Chuang, J. and Turner, W. (2008). Cubist algebras. Advances in Mathematics, 217(4), pp. 1614-1670. doi: 10.1016/j.aim.2007.06.017

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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.

Publication Type: Article
Publisher Keywords: cubist, tilings
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
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