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Coverings of directed graphs and crossed products of C*-algebras by coactions of homogeneous spaces

Journal Article


Abstract


  • We show that if p : F → E is a covering of directed graphs, then the Cuntz-Krieger algebra C* (F) of F can be viewed as a crossed product of C* (E) by a coaction of a homogeneous space for the fundamental group π1(E). Combining this result with information about Cuntz-Krieger algebras gives some interesting corollaries which suggest conjectures about crossed products by coactions of homogeneous spaces of discrete groups. We then prove these conjectures.

Publication Date


  • 2003

Citation


  • Deicke, K., Pask, D., & Raeburn, I. (2003). Coverings of directed graphs and crossed products of C*-algebras by coactions of homogeneous spaces. International Journal of Mathematics, 14(7), 773-789. doi:10.1142/S0129167X03001995

Scopus Eid


  • 2-s2.0-0141790845

Start Page


  • 773

End Page


  • 789

Volume


  • 14

Issue


  • 7

Abstract


  • We show that if p : F → E is a covering of directed graphs, then the Cuntz-Krieger algebra C* (F) of F can be viewed as a crossed product of C* (E) by a coaction of a homogeneous space for the fundamental group π1(E). Combining this result with information about Cuntz-Krieger algebras gives some interesting corollaries which suggest conjectures about crossed products by coactions of homogeneous spaces of discrete groups. We then prove these conjectures.

Publication Date


  • 2003

Citation


  • Deicke, K., Pask, D., & Raeburn, I. (2003). Coverings of directed graphs and crossed products of C*-algebras by coactions of homogeneous spaces. International Journal of Mathematics, 14(7), 773-789. doi:10.1142/S0129167X03001995

Scopus Eid


  • 2-s2.0-0141790845

Start Page


  • 773

End Page


  • 789

Volume


  • 14

Issue


  • 7