Home Mathematics On freely generated semigraph C*-algebras
Article
Licensed
Unlicensed Requires Authentication

On freely generated semigraph C*-algebras

  • Bernhard Burgstaller EMAIL logo
Published/Copyright: April 27, 2016
Become an author with De Gruyter Brill
Author Information Explore this Subject
Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

For special universal C*-algebras associated to k-semigraphs we present the universal representations of these algebras, prove a Cuntz–Krieger uniqueness theorem, and compute the K-theory. These C*-algebras seem to be the most universal Cuntz–Krieger like algebras naturally associated to k-semigraphs. For instance, the Toeplitz Cuntz algebra is a proper quotient of such an algebra.

Keywords: higher rank; graph algebra; semigraph; ultragraph; labelled graph; K-theory
MSC: Primary 46L05; 46L80

  1. This paper has been communicated by Werner Timmermann

References

[1] Bates, T.–-Pask, D.: C*-algebras of labelled graphs, J. Operator Theory 57 (2007), 207–226.Search in Google Scholar

[2] Brenken, B.–-Niu, Z.: The C*-algebra of a partial isometry, Proc. Amer. Math. Soc. 140 (2012), 199–206.10.1090/S0002-9939-2011-10988-2Search in Google Scholar

[3] Burgstaller, B.: The K-theory of certain C*-algebras endowed with gauge actions, J. Funct. Anal. 256 (2009), 1693–1707.10.1016/j.jfa.2009.01.026Search in Google Scholar

[4] Burgstaller, B.: A Cuntz–Krieger uniqueness theorem for semigraph C*-algebras, Banach J. Math. Anal. 6 (2012), 38–57.10.15352/bjma/1342210159Search in Google Scholar

[5] Cho, I.–-Jorgensen, P.: C*-subalgebras generated by partial isometries, J. Math. Phys. 50 (2009), Article ID 023516. http://scitation.aip.org/content/aip/journal/jmp/50/2/10.1063/1.305658810.1063/1.3056588Search in Google Scholar

[6] Cuntz, J.: Simple C*-algebras generated by isometries, Comm. Math. Phys. 57 (1977), 173–185.10.1007/BF01625776Search in Google Scholar

[7] Cuntz, J.: K-theory for certain C*-algebras, Ann. of Math. (2) 113 (1981), 181–197.10.2307/1971137Search in Google Scholar

[8] Cuntz, J.–-Krieger, W.: A class of C*-algebras and topological Markov chains, Invent. Math. 56 (1980), 251–268.10.1007/BF01390048Search in Google Scholar

[9] Kumjian, A.–-Pask, D.: Higher rank graph C*-algebras, New York J. Math. 6 (2000), 1–20.Search in Google Scholar

[10] Raeburn, I.–-Sims, A.: Product systems of graphs and the Toeplitz algebras of higher-rank graphs, J. Operator Theory 53 (2005), 399–429.Search in Google Scholar

[11] Tomforde, M.: A unified approach to Exel-Laca algebras and C*-algebras associated to graphs, J. Operator Theory 50 (2003), 345–368.Search in Google Scholar

[12] Toms, A. S.: On the classification problem for nuclear C*-algebras, Ann. of Math. (2) 167 (2008), 1029–1044.10.4007/annals.2008.167.1029Search in Google Scholar

Received: 2012-10-29
Accepted: 2013-5-22
Published Online: 2016-4-27
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Research Article
  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
  8. Lexico groups and direct products of lattice ordered groups
  9. Research Article
  10. Values of limit periodic sequences and functions
  11. Research Article
  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
  15. Research Article
  16. On some modification of Darboux property
  17. Research Article
  18. Separating sets by peripherally continuous functions
  19. Research Article
  20. Persistence and extinction of a stochastic delay predator-prey model in a polluted environment
  21. Research Article
  22. On O’Malley preponderantly continuous functions
  23. Research Article
  24. Inequalities for the normalized Jensen functional with applications
  25. Research Article
  26. Majorization of starlike and convex functions of complex order involving linear operators
  27. Research Article
  28. Fekete–Szegö problem for some starlike functions related to shell-like curves
  29. Research Article
  30. Central functions for classes of concave univalent functions
  31. Research Article
  32. Inclusion properties for classes of analytic functions associated with conic domains
  33. Research Article
  34. Uniqueness of meromorphic functions and nonlinear differential polynomials sharing a nonzero polynomial
  35. Research Article
  36. Solutions and constrained null-controllability for a differential-difference equation
  37. Research Article
  38. Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale
  39. Research Article
  40. Time periodic solutions for a sixth order nonlinear parabolic equation
  41. Research Article
  42. Some inequalities of trigonometric approximation in weighted Orlicz spaces
  43. Research Article
  44. Summation methods applied to Voronovskaya-type theorems for the partial sums of Fourier series and for Fejér operators
  45. Research Article
  46. Dichotomies for Orlicz spaces
  47. Research Article
  48. On freely generated semigraph C*-algebras
  49. Research Article
  50. Operators with a given part of the numerical range
  51. Research Article
  52. Characterization of quasi-continuity of multifunctions of two variables
  53. Research Paper
  54. Confidence regions in singular weakly nonlinear regression models with constraints
  55. Research Article
  56. Global stability of an SEI model for plant diseases
https://doi.org/10.1515/ms-2015-0133
Keywords for this article
higher rank; graph algebra; semigraph; ultragraph; labelled graph; K-theory

Articles in the same Issue

  1. Research Article
  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
  8. Lexico groups and direct products of lattice ordered groups
  9. Research Article
  10. Values of limit periodic sequences and functions
  11. Research Article
  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
  15. Research Article
  16. On some modification of Darboux property
  17. Research Article
  18. Separating sets by peripherally continuous functions
  19. Research Article
  20. Persistence and extinction of a stochastic delay predator-prey model in a polluted environment
  21. Research Article
  22. On O’Malley preponderantly continuous functions
  23. Research Article
  24. Inequalities for the normalized Jensen functional with applications
  25. Research Article
  26. Majorization of starlike and convex functions of complex order involving linear operators
  27. Research Article
  28. Fekete–Szegö problem for some starlike functions related to shell-like curves
  29. Research Article
  30. Central functions for classes of concave univalent functions
  31. Research Article
  32. Inclusion properties for classes of analytic functions associated with conic domains
  33. Research Article
  34. Uniqueness of meromorphic functions and nonlinear differential polynomials sharing a nonzero polynomial
  35. Research Article
  36. Solutions and constrained null-controllability for a differential-difference equation
  37. Research Article
  38. Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale
  39. Research Article
  40. Time periodic solutions for a sixth order nonlinear parabolic equation
  41. Research Article
  42. Some inequalities of trigonometric approximation in weighted Orlicz spaces
  43. Research Article
  44. Summation methods applied to Voronovskaya-type theorems for the partial sums of Fourier series and for Fejér operators
  45. Research Article
  46. Dichotomies for Orlicz spaces
  47. Research Article
  48. On freely generated semigraph C*-algebras
  49. Research Article
  50. Operators with a given part of the numerical range
  51. Research Article
  52. Characterization of quasi-continuity of multifunctions of two variables
  53. Research Paper
  54. Confidence regions in singular weakly nonlinear regression models with constraints
  55. Research Article
  56. Global stability of an SEI model for plant diseases
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 15.12.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2015-0133/html
Scroll to top button