Cubist Algebras

Article, Preprint, Unknown English OPEN
Chuang, J. ; Turner, W. (2007)
  • Publisher: Elsevier
  • Journal: volume 217, issue 4, pages 1,614-1,670 (issn: 0001-8708, eissn: 1090-2082)
  • Related identifiers: doi: 10.1016/j.aim.2007.06.017
  • Subject: QA | Mathematics(all) | Mathematics - Combinatorics | Mathematics | 20G05 | Mathematics - Representation Theory

<p>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. © 2007 Elsevier Inc. All rights reserved.</p>
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