On quantales that classify C * -algebras

David Kruml; Pedro Resende

Cahiers de Topologie et Géométrie Différentielle Catégoriques (2004)

  • Volume: 45, Issue: 4, page 287-296
  • ISSN: 1245-530X

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Kruml, David, and Resende, Pedro. "On quantales that classify $C^\ast $-algebras." Cahiers de Topologie et Géométrie Différentielle Catégoriques 45.4 (2004): 287-296. <http://eudml.org/doc/91687>.

@article{Kruml2004,
author = {Kruml, David, Resende, Pedro},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {-algebras; involutive quantales},
language = {eng},
number = {4},
pages = {287-296},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {On quantales that classify $C^\ast $-algebras},
url = {http://eudml.org/doc/91687},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Kruml, David
AU - Resende, Pedro
TI - On quantales that classify $C^\ast $-algebras
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2004
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 45
IS - 4
SP - 287
EP - 296
LA - eng
KW - -algebras; involutive quantales
UR - http://eudml.org/doc/91687
ER -

References

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  1. [1] F. Borceux, J. Rosický, G. Van den Bossche.Quantales and C*algebras, J. London Math. Soc.40 (1989) 398-404. Zbl0705.06009MR1053610
  2. [2] R. Giles, H. Kummer, A non-commutative generalisation of topology, Indiana Univ. Math. J.21 (1971) 91-102. Zbl0219.54003MR293408
  3. [3] D. Kruml, Spatial quantales, Appl. Categ. Structures10 (2002) 49-62. Zbl0999.06015MR1883084
  4. [4] D. Kruml, J.W. Pelletier, P. Resende, J. Rosický, On quantales and spectra of C*-algebras, Appl. Categ. Structures11 (2003) 543-560; arXiv: math. OA/0211345. Zbl1044.46052MR2017650
  5. [5] C.J. Mulvey, &, Rend. Circ. Mat. Palermo (2) Suppl. (1986) 99— 104. Zbl0633.46065MR853151
  6. [6] C.J. Mulvey, Quantales, Invited Lecture, Summer Conference on Locales and Topological Groups, Curaçao, 1989. 
  7. [7] C.J. Mulvey, Quantales, in: M. Hazewinkel (Ed.), The Encyclopaedia of Mathematics, third supplement, Kluwer Academic Publishers, 2002, pp. 312-314. 
  8. [8] C.J. Mulvey, J.W. Pelletier, A quantisation of the calculus of relations, Canad. Math. Soc. Conf. Proc.13 (1992) 345-360. Zbl0793.06008MR1192157
  9. [9] C.J. Mulvey, J.W. Pelletier, On the quantisation of points, J. Pure Appl. Algebra159 (2001) 231-295. Zbl0983.18007MR1828940
  10. [10] C.J. Mulvey, J.W. Pelletier, On the quantisation of spaces, J. Pure Appl. Algebra175 (2002) 289-325. Zbl1026.06018MR1935983
  11. [11] C.J. Mulvey, P. Resende, A noncommutative theory of Penrose tilings; arXiv:math.CT/0306361. Zbl1087.52509MR2150184
  12. [12] J. Paseka, J. Rosický, Quantales, in: B. Coecke, D. Moore, A. Wilce, (Eds.), Current Research in Operational Quantum Logic: Algebras, Categories and Languages, Fund. Theories Phys., vol. 111, Kluwer Academic Publishers, 2000, pp. 245-262. Zbl0962.06017MR1907153
  13. [13] J.W. Pelletier, J. Rosický, Simple involutive quantales, J. Algebra195 (1997) 367-386. Zbl0894.06005MR1469630
  14. [14] P. Resende, From algebras to quantales and back, Talk at the Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories, Fields Institute, Toronto, September 23-28, 2002, http://www.fields.utoronto.ca/programs/scientific/02-03/galois_and_hopf/. 
  15. [15] P. Resende, Sup-lattice 2-forms and quantales, J. Algebra276 (2004) 143-167; arXiv:math.RA/0211320. Zbl1059.06011MR2054391
  16. [16] J. Rosický, Multiplicative lattices and C*-algebras, Cahiers de Top. et Géom. Diff. Cat.XXX-2 (1989) 95—110. Zbl0676.46047MR1004734

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