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Spectral Triples on Inductive Limit C*-Algebras

Jacopo Bassi
Friday, June 24, 2016 - 11:00

The first classification result for infinite-dimensional C*-algebras is a natural generalization of the finite-dimensional case when considering M_n(C) as an inductive limit of itself over the identity *-homomorphism. It concerns the relationship between AF-algebras and Bratteli diagrams, or equivalently, K_0-groups. Adding more K-theoretical data a larger class of inductive limit C*-algebras can be classified and other inductive limits have been proven to be not in the Elliott conjecture class. 

In the category of C*-algebras, a central role is played by the strongly self-absorbing ones and in the finite case the only known examples of such are inductive limit C*-algebras. 

A geometric analysis of these objects amounts first of all to the construction of spectral triples on them. We discuss a way to do that for a class of C*-algebras that covers the finite strongly self-absorbing case using the interplay between the inductive limit process and the eigenspace decomposition of the Dirac operators considered.

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