Cubist algebras
Copyright policy )Cubist algebras
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.
- University of Bristol (UoB) United Kingdom
- City, University of London United Kingdom
- University of Oxford United Kingdom
- University of Bristol United Kingdom
quasi-hereditary structures, Mathematics(all), cubist, Cubist, tilings, cubical complexes, 510, Tilings in \(n\) dimensions (aspects of discrete geometry), FOS: Mathematics, Mathematics - Combinatorics, cubist algebras, Representation Theory (math.RT), QA, 20G05, Quadratic and Koszul algebras, Representations of finite symmetric groups, Koszul algebras, tilings of Euclidean space, representations of symmetric groups, 004, Tilings, quiver algebras, Representations of quivers and partially ordered sets, Homological functors on modules (Tor, Ext, etc.) in associative algebras, Combinatorics (math.CO), Mathematics, cellular bases, Mathematics - Representation Theory
quasi-hereditary structures, Mathematics(all), cubist, Cubist, tilings, cubical complexes, 510, Tilings in \(n\) dimensions (aspects of discrete geometry), FOS: Mathematics, Mathematics - Combinatorics, cubist algebras, Representation Theory (math.RT), QA, 20G05, Quadratic and Koszul algebras, Representations of finite symmetric groups, Koszul algebras, tilings of Euclidean space, representations of symmetric groups, 004, Tilings, quiver algebras, Representations of quivers and partially ordered sets, Homological functors on modules (Tor, Ext, etc.) in associative algebras, Combinatorics (math.CO), Mathematics, cellular bases, Mathematics - Representation Theory
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