We realize Kellendonk's C*-algebra of an aperiodic tiling as the tight C*-algebra of the inverse semigroup associated to the tiling, thus providing further evidence that the tight C*-algebra is a good candidate to be the natural associative algebra to go along with an inverse semigroup.

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Keywords C*-algebra, Inverse semigroup, Tight representations, Tiling
Persistent URL dx.doi.org/10.1007/s00233-011-9359-x
Journal Semigroup Forum
Exel, R. (Ruy), Gonçalves, D. (Daniel), & Starling, C. (2012). The tiling C*-algebra viewed as a tight inverse semigroup algebra. Semigroup Forum, 84(2), 229–240. doi:10.1007/s00233-011-9359-x