C*-Algebras over Topological Spaces: The Bootstrap Class

Abstract

We carefully define and study C*-algebras over topological spaces, possibly non-Hausdorff, and review some relevant results from point-set topology along the way. We explain the triangulated category structure on the bivariant Kasparov theory over a topological space. We introduce and describe an analogue of the bootstrap class for C*-algebras over a finite topological space.

Final version, very minor changes

References in corpus (2)

• Homological algebra in bivariant K-theory and other triangulated categories
• Dualities in equivariant Kasparov theory

Cited by in corpus (26)

• Homological algebra in bivariant K-theory and other triangulated categories
• The complete classification of unital graph $C^{\ast }$-algebras: Geometric and strong
• Geometric classification of graph $C^{\ast }$-algebras over finite graphs
• Inverse semigroup actions on groupoids
• E-Theory for C*-algebras over topological spaces
• Inverse semigroup actions as groupoid actions
• Strong classification of extensions of classifiable C*-algebras
• Universal coefficient theorems for C*-algebras over finite topological spaces
• The K-theoretical range of Cuntz-Krieger algebras
• Classifying $C^{\ast }$-algebras with both finite and infinite subquotients
• Stone duality and quasi-orbit spaces for generalised C*-inclusions
• Amplified graph C*-algebras
• Classification of real rank zero, purely infinite C*-algebras with at most four primitive ideals
• Projective dimension in filtrated K-theory
• Absorbing representations with respect to closed operator convex cones
• Classification of graph C*-algebras with no more than four primitive ideals
• Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras
• Reconstructing the Bost--Connes semigroup actions from K-theory
• Homotopy-theoretic E-theory and n-order
• Classification of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras
• The nuclear dimension of graph C*-algebras
• One-parameter continuous fields of Kirchberg algebras with rational K-theory
• Graph $C^{\ast }$-algebras with a $T_1$ primitive ideal space
• Identifying AF-algebras that are graph C*-algebras
• Quasi-invariant lifts of completely positive maps for groupoid actions
• Continuous C*-algebras over topological spaces