We show how to recover a discrete twist over an ample Hausdorff groupoid from a pair consisting of an algebra and what we call a quasi-Cartan subalgebra. We identify precisely which twists arise in this way (namely, those that satisfy the local bisection hypothesis), and we prove that the assignment of twisted Steinberg algebras to such twists and our construction of a twist from a quasi-Cartan pair are mutually inverse. We identify the algebraic pairs that correspond to effective groupoids and to principal groupoids. We also indicate the scope of our results by identifying large classes of twists for which the local bisection hypothesis holds automatically.
Abstract. We characterize the class of RFD C * -algebras as those containing a dense subset of elements that attain their norm under a nite-dimensional representation. We show further that this subset is the whole space precisely when every irreducible representation of the C * -algebra is nite-dimensional, which is equivalent to the C * -algebra having no simple in nite-dimensional AF subquotient. We apply techniques from this proof to show the existence of elements in more general classes of C * -algebras whose norms in nite-dimensional representations t certain prescribed properties.
We say that a contractive Hilbert space operator is universal if there is a natural surjection from its generated C * -algebra to the C * -algebra generated by any other contraction. A universal contraction may be irreducible or a direct sum of (even nilpotent) matrices; we sharpen the latter fact and its proof in several ways, including von Neumann-type inequalities for noncommutative *-polynomials. We also record properties of the unique C * -algebra generated by a universal contraction, and we show that it can be used similarly to C * (F 2 ) in various Kirchberg-like reformulations of Connes' Embedding Problem (some known, some new). Finally we prove some analogous results for universal C * -algebras of row contractions and universal Pythagorean C *algebras.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.