Open AccessA Noncommutative Theory of Penrose Tilings
Author(s) -
Christopher J. Mulvey,
Pedro Resende
Publication year - 2005
Publication title -
international journal of theoretical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.337
H-Index - 65
eISSN - 0020-7748
pISSN - 1572-9575
DOI - 10.1007/s10773-005-3997-2
Subject(s) - noncommutative geometry , mathematics , substitution tiling , pure mathematics , quotient , cantor set , penrose tiling , representation (politics) , space (punctuation) , plane (geometry) , algebra over a field , discrete mathematics , quasicrystal , geometry , politics , political science , law , linguistics , philosophy
Considering quantales as generalised noncommutative spaces, we address as an example a quantale Pen based on the Penrose tilings of the plane. We study in general the representations of involutive quantales on those of binary relations, and show that in the case of Pen the algebraically irreducible representations provide a complete classification of the set of Penrose tilings from which its representation as a quotient of Cantor space is recovered.
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