Abstract:
In joint work with Farsi, Kang, and Packer, we have constructed a representation of a higher-rank graph C*-algebra C*(Λ) on L^2(Λ^\infty, M), where Λ^\infty is the space of infinite paths in the higher-rank graph \Lambda and M is a canonical Borel measure on Λ^\infty. This representation gives rise to a wavelet-type decomposition of L^2(Λ^\infty, M); in joint work with Farsi, Kang, Julien, and Packer, we have discovered that this wavelet-type decomposition is closely related to the spectral triples and Dirac operators on Λ^\infty studied by Pearson and Bellissard and by Julien and Savinien. In this talk, we will explain these connections, and (time permitting) also describe the relationship between the FGKP wavelet decomposition and another spectral triple for C*(Λ), which was first described by Consani and Marcolli for Cuntz-Krieger algebras O_A.