Cubist Algebras

Joseph Chuang, W Turner

Research output: Contribution to journalArticle (Academic Journal)peer-review

12 Citations (Scopus)

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.
Translated title of the contributionCubist Algebras
Original languageEnglish
Pages (from-to)1614 - 1670
Number of pages57
JournalAdvances in Mathematics
Volume217 (4)
DOIs
Publication statusPublished - Mar 2008

Bibliographical note

Publisher: Elsevier

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