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Submitted
August 3, 2022
Accepted
October 3, 2023
Published
November 30, 2023
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Abstract

Let Λ and Γ be row finite k-graphs without sources. We show that ∗-algebra homomorphisms ϕ : KPC(Λ) → KPC(Γ) extend to ∗-algebra homomorphisms ϕ¯ : C∗(Λ) → C∗(Γ). We also examine necessary and sufficient conditions for algebra homomorphisms between complex Kumjian-Pask algebras KPC(Λ) and KPC(Γ) which are ∗-preserving.

Keywords

Kumjian-Pask algebra Leavitt path algebra Homomorphism k-graph

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How to Cite
Rosjanuardi, R., Mulyaning Asih, E. C., & Masta, A. A. (2023). Homomorphisms of Complex Kumjian-Pask Algebras. Journal of the Indonesian Mathematical Society, 29(3), 328–337. https://doi.org/10.22342/jims.29.3.1262.328-337
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References

  1. G. Abrams and M. Tomforde, Isomorphism and Morita equivalence of graph algebras, Transaction of American Mathematical Society, 363 (2011), 3733-3767.
  2. G. Abrams G, G. A. Pino, The Leavitt path algebra of a graph, Journal of Algebra, 293(2)
  3. (2005), 319-334.
  4. J. H. Brown and A. an Huef, The socle and simplicity of a Kumjian-Pask algebra, Communication in Algebra, 43(7)(2015), 2703-2723.
  5. L. O. Clark, C. Flynn, and A. an Huef, Kumjian-Pask algebras of locally convex higher-rank
  6. graphs, J. Algebra, 399 (2014), 445-474.
  7. L. O. Clark and Y. E. P. Pangalela, Kumjian-Pask algebras of finitely-aligned higher-rank
  8. graphs, J. Algebra, 482 (2017), 364-397.
  9. L. O. Clark, C. G. Canto, A. Nasr-Isfahani, The cycline subalgebra of a Kumjian-Pask
  10. algebra, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 145 (5)
  11. (2017), 1969–1980.
  12. S. M. Gozali, R. Rosjanuardi and I. Yusnitha, On the center of Kumjian-Pask algebras
  13. associated to finitely aligned k-graph, AIP Conference Proceedings, 1830(070029) (2017).
  14. M. Kashoul-Radjabzadeh, H. Larki, On the Decomposable C*–algebras and Kumjian-Pask
  15. algebras, Journal of Advanced Mathematical Modeling, 8(2) (2018), 94-112.
  16. M. Kashoul-Radjabzadeh, H. Larki, and A. Aminpour, Prime and primitive Kumjian–Pask
  17. algebras, Journal of Algebra and Its Applications 16(09) (2017).
  18. A. Kumjian, D. Pask , Higher rank graph C∗-algebras, New York Journal of Mathematics,
  19. (2000), 1-20.
  20. A. Kumjian A, D. Pask, I. Raeburn , Cuntz-Krieger algebras of directed graphs, . Pacific
  21. Journal of Mathematics, 184, (1998), 162-274.
  22. H. Larki, Purely infinite simple Kumjian-Pask algebras, Forum Math., 30(1) (2018),253-268.
  23. G. A. Pino, J. Clark, A. An Huef, I. Raeburn, Kumjian-Pask algebras of higher rank graphs,
  24. Transaction of American Mathematical Society, 365(7) (2013), 3613-3641.
  25. S. C. Power, Subalgebras of graph C∗-algebras, Operator Theory: Advances and Applications, 181 (2008), 3-32.
  26. I. Raeburn, Graph algebras. Rhode Island, RI, USA: CBMS-NSF MA Vol.103, 2005.
  27. R. Rosjanuardi, Complex Kumjian-Pask algebras, Acta Mathematica Sinica, 29(11) (2013),
  28. -2078
  29. R. Rosjanuardi and I. Yusnitha, Kumjian-Pask Algebras of Desourcification, AIP Conference
  30. Proceedings, 1708(060006) (2016).
  31. R. Rosjanuardi, Some notes on complex Kumjian-Pask algebras of finitelt aligned k-graph,
  32. AIP Conference Proceedings, 1830(070027) (2017).
  33. R. Rosjanuardi, Representing k-graphs as Matrix Algebras, Journal of Physics: Conference
  34. Series, 1013(012207) (2018).
  35. R. Rosjanuardi and S. M. Gozali, Ideals In Kumjian-Pask Algebras of Finite k-Graphs, Far
  36. East Journal of Mathematical Sciences, 103(4) (2018), 757-766.
  37. I. Yusnitha and R. Rosjanuardi, Kumjian-Pask Algebras of 2-graphs, AIP Conference Proceedings, 1708(060010) (2016)