A noncommutative theory of Penrose tilings ∗

@inproceedings{Mulvey2003ANT,
  title={A noncommutative theory of Penrose tilings ∗},
  author={Christopher J. Mulvey and Pedro Resende},
  year={2003}
}
Considering quantales as generalised noncommutative spaces, we address as an example a quantale Pen based on the Penrose tilings of the plane. We study in general the representations of involutive quantales on those of binary relations, and show that in the case of Pen the algebraically irreducible representations provide a complete classification of the set of Penrose tilings from which its representation as a quotient of Cantor space is recovered. 

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Showing 1-10 of 24 references

On the quantisation of points

  • C. J. Mulvey, J. W. Pelletier
  • J. Pure Appl. Algebra 159
  • 2001
Highly Influential
8 Excerpts

The spectral theory of commutative C*algebras: the constructive Gelfand-Mazur theorem

  • B. Banaschewski, C. J. Mulvey
  • Quaest. Math. 23
  • 2000
Highly Influential
6 Excerpts

The spectral theory of commutative C*algebras: the constructive spectrum

  • B. Banaschewski, C. J. Mulvey
  • Quaest. Math. 23
  • 2000
Highly Influential
6 Excerpts

Tilings and Patterns

  • B. Grümbaum, G. C. Shepard
  • Freeman, New York
  • 1989
Highly Influential
3 Excerpts

Introduction to Operator Space Theory

  • G. Pisier
  • Cambridge University Press
  • 2003
1 Excerpt

From algebras to quantales and back

  • P. Resende
  • Talk at the Workshop on Categorical Structures…
  • 2002
1 Excerpt

On the quantisation of spaces

  • C. J. Mulvey, J. W. Pelletier
  • J. Pure Appl. Algebra 175
  • 2002
2 Excerpts

Points of quantales

  • D. Kruml
  • Ph.D. Thesis, Masaryk University, Brno
  • 2002
1 Excerpt

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