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Realization of a simple higher‐dimensional noncommutative torus as a transformation group C*‐algebra
Author(s) -
ItzáOrtiz Benjamín A.,
Phillips N. Christopher
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn001
Subject(s) - mathematics , noncommutative geometry , crossed product , realization (probability) , torus , homeomorphism (graph theory) , pure mathematics , simple (philosophy) , group (periodic table) , group algebra , algebra over a field , combinatorics , philosophy , statistics , chemistry , geometry , organic chemistry , epistemology
Let θ be a nondegenerate skew symmetric real d × d matrix, and let A θ be the corresponding simple higher‐dimensional noncommutative torus. Suppose that d is odd, or that d ⩾4 and the entries of θ are not contained in a quadratic extension of ℚ. Then A θ is isomorphic to the transformation group C*‐algebra obtained from a minimal homeomorphism of a compact connected one‐dimensional space locally homeomorphic to the product of the interval and the Cantor set. The proof uses classification theory of C*‐algebras.