The Noncommutative Space of Penrose Tilings

Francesco D’Andrea ()
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Francesco D’Andrea: University of Naples Federico II, Department of Mathematics and Applications “Renato Caccioppoli”

Chapter Chapter 6 in A Guide to Penrose Tilings, 2023, pp 157-190 from Springer

Abstract: Abstract In this chapter, we study the space parameterizing inequivalent Penrose tilings from the point of view of Noncommutative Geometry. This chapter is a self-contained introduction to Bratteli diagrams, AF equivalence relations, AF algebras and their K-theory, and their use in the classification of minimal Cantor systems, such as the one parameterizing Penrose tilings. We will take for granted some basic results about K-theory and assume that the reader has some familiarity with C*-algebras.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-28428-1_6

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DOI: 10.1007/978-3-031-28428-1_6

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