NCG seminar

[Emanuele Tuillier Illingworth]

*"NON-COMMUTATIVE GEOMETRY" SEMINAR 
<https://www.math.sissa.it/content/non-commutative-geometry-seminars>*

Thursday 23 June 2016 at 11:00
Venue: SISSA, Room 138

Jacopo Bassi (SISSA)
"Spectral Triples on Inductive Limit C*-Algebras"

Abstract:
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.