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

El Kacimi Alaoui, A.; Parthasarathy, R.

doi:10.1090/S0002-9939-02-06693-5

Trace splittings in $C^*$-algebras of tiling systems via colourings
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by A. El Kacimi Alaoui and R. Parthasarathy PDF

Proc. Amer. Math. Soc. 131 (2003), 1191-1204 Request permission

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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