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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Trace splittings in $C^*$-algebras of tiling systems via colourings


Authors: A. El Kacimi Alaoui and R. Parthasarathy
Journal: Proc. Amer. Math. Soc. 131 (2003), 1191-1204
MSC (1991): Primary 46L89, 52C23
Published electronically: July 26, 2002
MathSciNet review: 1948111
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Abstract: Tiles of a hierarchical tiling system are coloured with given colours. The resulting system implements colour symmetries and prescribed frequencies and is itself a hierarchical system whose prototile types admit an elegant description. The frequencies of occurrence of colours is interpreted using the unique trace on the $C^*$-algebra of the given tiling system and the trace on the $C^*$-algebra of the coloured tiling system.


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Additional Information

A. El Kacimi Alaoui
Affiliation: LAMATH, Le Mont Houy, Université de Valenciennes, 59313 Valenciennes Cedex 9, France
Email: elkacimi@univ-valenciennes.fr

R. Parthasarathy
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 - 005, India
Email: sarathy@math.tifr.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06693-5
PII: S 0002-9939(02)06693-5
Received by editor(s): July 3, 2001
Received by editor(s) in revised form: November 16, 2001
Published electronically: July 26, 2002
Additional Notes: The second author is grateful to LAMATH, Laboratoire de Mathématiques, Université de Valenciennes et du Hainaut Cambrésis for their hospitality during his stay when this work was done.
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society