A noncommutative theory of penrose tilings

International Journal of Theoretical Physics

Volumn 44, Issue 6, 2005, Pages 655-689

  Mulvey, Christopher J ^a   Resende, Pedro ^b  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

^b INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Noncommutative logic; Noncommutative space; Penrose tiling; Quantale; Relational point; Relational representation

Indexed keywords

EID: 22044452847     PISSN: 00207748     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10773-005-3997-2     Document Type: Article

References (30)

1. Abramsky, S. and Vickers, S. (1993). Mathematical Structures in Computer Science 3, 161-227.
2. Amira, H., Coecke, B., and Stubbe, I. (1998). Helvetica Physica Acta 71, 554-572.
3. Banaschewski, B. and Mulvey, C. J. (2000a). Quaestiones Mathematicae 23, 425-464.
4. Banaschewski, B. and Mulvey, C. J. (2000b). Quaestiones Mathematicae 23, 465-488.
5. Banaschewski, B. and Mulvey, C. J. (To appear). A globalisation of Gelfand duality.
6. Coecke, B. and Stubbe, I. (1999). International Journal of Theoretical Physics 38, 3269-3281.
7. Connes, A. (1994). Noncommutative Geometry, Academic Press.
8. Giles, R. and Kummer, H. (1971). Indiana University Mathematics Journal 21, 91-102.
9. Grümbaum, B. and Shepard, G. C. (1989). Tilings and Patterns, Freeman, New York.
10. Johnstone, P. (1982). Stone Spaces, Cambridge Studies in Advanced Mathematics, vol. 3, Cambridge University Press.
11. Joyal, A. and Tierney, M. (1984). An Extension of the Galois Theory of Grothendieck, Memoirs of the American Mathematical Society, vol. 309, American Mathematical Society.
12. Kruml, D. (2002). Applied Categorical Structures 10, 49-62.
13. Kruml, D. (2002). Ph.D. Thesis, Masaryk University, Brno.
14. Kruml, D., Pelletier, J. W., Resende, P., and Rosicky, J. (2003). Applied Categorical Structures 11, 543-560; arXiv:math.OA/0211345.
15. Kruml, D. and Resende, P. (2004). Cahiers de Top. et Geom. Diff. Cat. XLV-4, 287-296; arXiv:math.OA/0404001.
16. Mulvey, C. J. (1986). Rendiconti del Circolo Matematico di Palermo 2(Suppl.) 99-104.
17. Mulvey, C. J. (1989). Quantales, Invited Lecture, Summer Conference on Locales and Topological Groups, Curaçao.
18. Mulvey, C. J. (2002). Quantales. In The Encyclopaedia of Mathematics, M. Hazewinkel, ed., 3rd supplement, Kluwer Academic Publishers, 2002, pp. 312-314.
19. Mulvey, C. J. and Pelletier, J. W. (1992). Canadian Mathematical Society Conference Proceeding 13, 345-360.
20. Mulvey, C. J. and Pelletier, J. W. (2001). Journal of Pure and Applied Algebra 159, 231-295.
21. Mulvey, C. J. an Pelletier, J. W. (2002). Journal of Pure and Applied Algebra 175, 289-325.
22. Paseka, J. and Rosický, J. (2000). Quantales, In Current Research in Operational Quantum Logic: Algebras, Categories and Languages, B. Coecke, D. Moore, A. Wilce, eds., Fundamental Theories of Physics, vol. 111, Kluwer Academic Publishers, pp. 245-262.
23. Pelletier, J. W. and Rosický, J. (1997). Journal of Algebra 195, 367-386.
24. Pisier, G. (2003). Introduction to Operator Space Theory, Cambridge University Press.
25. Resende, P. (1999). Modular specification of concurrent systems with observational logic. In Proceedings of WADT98, Lecture Notes in Computer Science, J.L. Fiadeiro, ed., vol. 1589, Springer, Berlin, pp. 307-321.
26. Resende, P. (2000). Quantales and observational semantics. In Current Research in Operational Quantum Logic: Algebras, Categories and Languages, B. Coecke, D. Moore, A. Wilce, eds., Fundamental Theories of Physics, vol. 111, Kluwer Academic Publishers, pp. 263-288.
27. Resende, P. (2001). Theoretical Computer Science 254, 95-149.
28. Resende, P. (2002). Journal of Pure and Applied Algebra 173, 87-120.
29. Resende, P. (2004). Journal of Algebra 276, 143-167; arXiv:math.RA/ 0211320.
30. Resende, P. and Vickers, S. J. (2003). Theoretical Computer Science 305, 311-346.