Cubist Algebras

Joseph Chuang; W Turner

doi:10.1016/j.aim.2007.06.017

Cubist Algebras

Joseph Chuang
, W Turner

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

13 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.

Original language	English
Pages (from-to)	1614 - 1670
Number of pages	57
Journal	Advances in Mathematics
Volume	217 (4)
DOIs	https://doi.org/10.1016/j.aim.2007.06.017
Publication status	Published - Mar 2008

Bibliographical note

Publisher: Elsevier

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10.1016/j.aim.2007.06.017

http://dx.doi.org/10.1016/j.aim.2007.06.017

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DERIVED EQUIVALENCES, BRAIS RELATIONS, AND STABILITY CONDITIONS
Chuang, J. (Principal Investigator)
1/10/04 → 1/10/09
Project: Research

Cite this

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title = "Cubist Algebras",

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.",

author = "Joseph Chuang and W Turner",

note = "Publisher: Elsevier",

year = "2008",

month = mar,

doi = "10.1016/j.aim.2007.06.017",

language = "English",

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pages = "1614 -- 1670",

journal = "Advances in Mathematics",

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T1 - Cubist Algebras

AU - Chuang, Joseph

AU - Turner, W

N1 - Publisher: Elsevier

PY - 2008/3

Y1 - 2008/3

N2 - 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.

AB - 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.

U2 - 10.1016/j.aim.2007.06.017

DO - 10.1016/j.aim.2007.06.017

M3 - Article (Academic Journal)

SN - 0001-8708

VL - 217 (4)

SP - 1614

EP - 1670

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Cubist Algebras

Abstract

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DERIVED EQUIVALENCES, BRAIS RELATIONS, AND STABILITY CONDITIONS

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