Invariant Means and Finite Representation Theory of $c*$-Algebras

By N. Brown. 2003

141 citations recorded by the source corpus.

Introduction Notation, definitions and useful facts Amenable traces and stronger approximation properties Examples and special cases Finite representations Applications and connections with other areas Bibliography.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/8acd990dabdd578cbf4d5457d45d939f7ae1dbdf

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In Computational Theory and Mathematics

Citations in the corpus

On the classification of simple amenable C*-algebras with finite decomposition rank (2015, unknown): “1 of [3]), the UHF algebra Q was replaced by a matrix algebra.”
Free entropy dimension in amalgamated free products (2006, background): “Indeed, if a II1-factor has a weak expectation relative to a weakly dense exact C∗-subalgebra then it must be hyperfinite [4].”
Strongly self-absorbing C*-algebras (2005, background): “9 of [1], which implies that D is tracially AF.”
Covering Dimension of C*-Algebras and 2-Coloured Classification (2015, background): “(ii) A has real rank zero, T (A) is a Bauer simplex and every τ ∈ T (A) is quasidiagonal in the sense of [9].”
ABOUT THE QWEP CONJECTURE (2003, background): “Brown [ Br1 ][Br2] studied various approximation properties of traces on C ∗ -”
Regularity properties in the classification program for separable amenable C*-algebras (2007, background): “) One can also verify the hypotheses of Lin’s classification theorem for many real rank zero C-algebras with unique trace ([4]), always with the assumption, indirectly, of strict comparison.”
Subalgebras of simple AF-algebras (2018, methodology): “See [9] or Chapter 6 of [10] for a detailed treatment of amenable traces.”
On the Classification of Simple Z‐Stable C*‐Algebras with Real Rank Zero and Finite Decomposition Rank (2005, result): “) Similar results were obtained in [1] and [11], under the additional condition that the algebras have only countably many extremal tracial states.”
Quasidiagonality of nuclear C*-algebras (2015, background): “Traces which can be witnessed by quasidiagonal approximations are called quasidiagonal (see Definition 1.2 below); these were introduced and systematically investigated in [10].”
STRUCTURE OF NUCLEAR C*-ALGEBRAS: FROM QUASIDIAGONALITY TO CLASSIFICATION AND BACK AGAIN (2017, unknown): “Nathanial P. Brown (2006).”