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arXiv · 0710.5457

Cubist Algebras

J. Chuang·W. Turner
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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.

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J. Chuang, W. Turner. 2007-10-29. Cubist Algebras. https://arxiv.org/abs/0710.5457

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