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Journal of Function Spaces
Volume 2016, Article ID 9639875, 8 pages
http://dx.doi.org/10.1155/2016/9639875
Research Article

On Cluster -Algebras

Department of Mathematics and Computer Science, St. John’s University, 8000 Utopia Parkway, Queens, New York, NY 11439, USA

Received 4 February 2016; Accepted 18 May 2016

Academic Editor: Gelu Popescu

Copyright © 2016 Igor V. Nikolaev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Fomin and A. Zelevinsky, “Cluster algebras I: foundations,” Journal of the American Mathematical Society, vol. 15, no. 2, pp. 497–529, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. S. Fomin, M. Shapiro, and D. Thurston, “Cluster algebras and triangulated surfaces. I. Cluster complexes,” Acta Mathematica, vol. 201, no. 1, pp. 83–146, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. L. K. Williams, “Cluster algebras: an introduction,” Bulletin of the American Mathematical Society, vol. 51, no. 1, pp. 1–26, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  4. E. G. Effros, Dimensions and C-Algebras, vol. 46 of CBMS Regional Conference Series in Mathematics, Conference Board of the Mathematical Sciences, 1981.
  5. B. Blackadar, K-Theory for Operator Algebras, vol. 5, MSRI Publications, Springer, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  6. O. Bratteli, “Inductive limits of finite dimensional C-algebras,” Transactions of the American Mathematical Society, vol. 171, pp. 195–234, 1972. View at Google Scholar · View at MathSciNet
  7. R. C. Penner, “The decorated Teichmüller space of punctured surfaces,” Communications in Mathematical Physics, vol. 113, no. 2, pp. 299–339, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. D. Mundici, “Farey stellar subdivisions, ultrasimplicial groups, and K0 of AF C*-algebras,” Advances in Mathematics, vol. 68, no. 1, pp. 23–39, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. F. P. Boca, “An AF algebra associated with the Farey tessellation,” Canadian Journal of Mathematics, vol. 60, no. 5, pp. 975–1000, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  10. D. Mundici, “Revisiting the Farey AF-algebra,” Milan Journal of Mathematics, vol. 79, no. 2, pp. 643–656, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. D. Mundici, “Recognizing the Farey-Stern-Brocot AF algebra, Dedicated to the memory of Renato Caccioppoli,” Rendiconti Lincei-Matematica e Applicazioni, vol. 20, pp. 327–338, 2009. View at Google Scholar
  12. C. Eckhardt, “A noncommutative Gauss map,” Mathematica Scandinavica, vol. 108, no. 2, pp. 233–250, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. G. Panti, “Prime ideals in free l -groups and free vector lattices,” Journal of Algebra, vol. 219, no. 1, pp. 173–200, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. E. G. Effros and C. L. Shen, “Approximately finite C*-algebras and continued fractions,” Indiana University Mathematics Journal, vol. 29, no. 2, pp. 191–204, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
  15. W. A. Veech, “The Teichmüller geodesic flow,” Annals of Mathematics. Second Series, vol. 124, no. 3, pp. 441–530, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  16. I. V. Nikolaev, “On a Teichmüller functor between the categories of complex tori and the Effros-Shen algebras,” New York Journal of Mathematics, vol. 15, pp. 125–132, 2009. View at Google Scholar · View at MathSciNet · View at Scopus
  17. I. Nikolaev, “Riemann surfaces and AF-algebras,” Annals of Functional Analysis, vol. 7, no. 2, pp. 371–380, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  18. I. Nikolaev, “Cluster C-algebras and knot polynomials,” http://arxiv.org/abs/1603.01180.
  19. I. Nikolaev, “K-theory of cluster C-algebras,” http://arxiv.org/abs/1512.00276.
  20. L. Bernstein, The Jacobi-Perron Algorithm—Its Theory and Application, vol. 207 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1971. View at MathSciNet
  21. A. Connes, “Von Neumann algebras,” in Proceedings of the International Congress of Mathematicians (ICM '78), pp. 97–109, Helsinki, Finland, 1978.
  22. W. P. Thurston, “On the geometry and dynamics of diffeomorphisms of surfaces,” Bulletin of the American Mathematical Society, vol. 19, no. 2, pp. 417–431, 1988. View at Publisher · View at Google Scholar · View at MathSciNet