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Jon Brown

Kansas State University



A generalized Cuntz-Krieger uniqueness theorem for k-graph algebras



Friday, March 28
1PM, 646 PGH



Abstract

In this talk, we present a uniqueness theorem for k-graph C*-algebras that requires neither an aperiodicity nor a gauge invariance assumption. Specifically, we prove that for the injectivity of a representation of a k-graph C*-algebra, it is sufficient that the representation be injective on a distinguished abelian C*-subalgebra. A crucial part of the proof is the application of an abstract uniqueness theorem, which says that such a uniqueness property follows from the existence of a jointly faithful collection of states on the ambient C*-algebra, each of which is the unique extension of a state on the distinguished abelian C*-subalgebra. This work is joint with Gabriel Nagy and Sarah Reznikoff.






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