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Dr. Dilian Yang


B.Sc.,(Sichuan Normal University), Ph.D. (Waterloo)
LT 9-116
Ext. 3042

Research Interests:
My main research interests are operator algebras and functional equations.
On operator algebras, I am currently interested in higher rank graph algebras. They are natural operator algebras associated with higher rank graphs, which are higher dimensional analogues of directed graphs. They have been attracting a great deal of attention recently. On one hand, there are some results generalized from graph algebras; on the other hand, they are significantly more complicated than graph algebras, and provide more intriguing operator algebras.
On functional equations, I am interested in studying them by applying harmonic analysis and representation theory. This gives close connections between functional equations and other areas.
Editorial Board: I am an editor for Banach Journal of Mathematical Analysis (2014 - )
Recent Publications:

 Operator Algebras:

  1. H. Li and D. Yang, Self-Similar k-Graph C*-algebras, to appear in International Mathematics Research Notices, 36 pages. DOI: 10.1093/imrn/rnz146.
  2. H. Li and D. Yang, KMS states of self-similar k–graph C*-algebras. J. Funct. Anal. 276 (2019), 3795–3831.
  3. H. Li and D. Yang, Boundary quotient C*-algebras of products of odometers, Canad. J. Math. 71 (2019), 183–212.
  4. D. Yang, Affine actions and the Yang-Baxter equation, Adv. Oper. Theory 3 (2018), 710–730.
  5. J. Brown, H. Li and D. Yang, Cartan subalgebras of topological graph algebras and k-graph C*-algebras. Münster J. Math. 10 (2017), 367–381. 
  6. D. Yang, the interplay between k-graphs and the Yang-Baxter equation, Journal of Algebra 451 (2016), 494-525.
  7. D. Yang, Cycline subalgebras of k-graph C*-algebras, Proceedings of the American Mathematical Society 144 (2016), 2959-2969.

  8. D. Yang, Factoriality and type classification of k-graph von Neumann algebras, Proceedings of the Edinburgh Mathematical Society 60 (2017), 499-518.

  9. D. Yang, Analytic free semigroup algebras and Hopf algebras, Houston J. Math. 42 (2016), 919-943. 

  10. D. Yang, Periodic k-graph algebras revisited, J. Aust. Math. Soc. 99 (2015), 267-286.
  11. A. Fuller and D. Yang, Nonself-adjoint 2-graph algebras, Transactions of the America Mathematical Society 367 (2015), 6199-6224.
  12. M. Kennedy and D. Yang, A non-self-adjoint Lebesgue decomposition, Analysis & PDE 7(2014), 497-512.
  13. M. Kennedy and D. Yang, The Hopf structure of some dual algebras, Integral Equations and Operator Theory 79 (2014), 191-217.
  14. D. Yang, Type III Von Neumann algebras associated with 2-graph, Bulletin of the London Mathematical Society 44 (2012), 675-686.
  15. D. Yang, Endomorphisms and modular theory of 2-graph C*-algebras, Indiana Univ. Math. J. 59 (2010) 495-520.
  16. K. R. Davidson, S. C. Power and D. Yang, Dilation theory for rank 2 graph algebras, J. Operator Theory 63 (2010), 245-270.
  17. K. R. Davidson and D. Yang, Representations of higher rank graph algebras, New York J. Math. 15 (2009), 169–198.
  18. K. R. Davidson and D. Yang, Periodicity in rank 2 graph algebras, Canad. J. Math. 61 (2009), 1239–1261.
  19. K. R. Davidson, S. C. Power and D. Yang, Atomic representations of rank 2 graph algebras, J. Funct. Anal. 255 (2008), 819–853.
  20. K. R. Davidson and D. Yang, A note on absolute continuity in free semigroup algebras, Houston J. Math. 34 (2008), 283–288.


 Functional Equations: 

  1. D. Ilisevi, A. Turnsek and D. Yang, Orthogonally Additive Mappings on Hilbert Modules, Studia Mathematica 221 (2014), 209-229.
  2. D. Yang, Functional equations and Fourier analysis, Canadian Mathematical Bulletin 56 (2013), 218-224.
  3. J. An and D. Yang, Nonabelian harmonic analysis and functional equations on compact groups, J. Lie Theory 21 (2011), 427-456. 
  4. D. Yang, The symmetrized sine additional formula, Aequationes Math. 82 (2011), 299-318.
  5. J. An and D. Yang, ALevi-Civita equation on compact groups and nonabelian Fourier analysis,  Integral Equations Operator Theory 66 (2010), 183-195.
  6. L. Li, D. Yang and W. Zhang, A note on iterative roots of PM functions, J. Math. Anal. Appl. 341 (2008), 1482–1486.
  7. D. Yang, Factorization of cosine functions on compact connected groups, Math. Z. 254 (2006), 655–674.
  8. D. Yang, Orthogonality spaces and orthogonally additive mappings, Acta. Math. Hungar. 113 (2006), 269-280.