Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590582 | Journal of Functional Analysis | 2014 | 20 Pages |
Abstract
We present a uniqueness theorem for k-graph Câ-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 Câ-algebra, it is sufficient that the representation be injective on a distinguished abelian Câ-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 Câ-algebra, each of which is the unique extension of a state on the distinguished abelian Câ-subalgebra.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jonathan H. Brown, Gabriel Nagy, Sarah Reznikoff,