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Cubist algebras

Chuang, J. and Turner, W. (2008). Cubist algebras. Advances in Mathematics, 217(4),

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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.

Publication Type: Article
Publisher Keywords: 0101 Pure Mathematics
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/7923
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