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C*‐Algebras Characterized by Ergodic Actions of the n ‐Torus
Author(s) -
Milnes Paul,
Walters Samuel
Publication year - 2000
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/s0024609300007207
Subject(s) - torus , mathematics , ergodic theory , isomorphism (crystallography) , action (physics) , commutative property , pure mathematics , geometry , physics , quantum mechanics , crystal structure , chemistry , crystallography
Using basic harmonic analysis on the n ‐torus, it is shown that the non‐commutative n ‐tori are the only primitive C*‐algebras (up to isomorphism) on which the n ‐torus T n acts freely and ergodically. An explicit construction recovers the generating unitaries in a natural way from the action. 2000 Mathematics Subject Classification 46L55.