Recursive subhomogeneous algebras

2001/01/18 by N. Christopher Phillips, Phillips, N. Christopher · 5 citations
Mathematics · #19B14 #19K14 #46L05 (Primary) 19A13 #46L80 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:19A13 #msc:19B14 #msc:19K14 #msc:46L05 #msc:46L80

paper · pdf · doi:10.48550/arxiv.math/0101156

29 pages, AMSLaTeX

arxiv created 2001/01/18 · openalex publication_date 2001/01/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursive subhomogeneous algebras, and they have an inductive description (through iterated pullbacks) which allows one to carry over from algebras of the form C (X, M_n) many of the constructions relevant in the study of the stable rank and K-theory of simple direct limits of homogeneous C*-algebras. Our characterization implies in particular that if A is a separable C*-algebra whose irreducible representations all have dimension at most N (for some finite N), and if for each n the space of n-dimensional irreducible representations has finite covering dimension, then A is a recursive subhomogeneous algebra. We demonstrate the good properties of this class by proving subprojection and cancellation theorems in it.

Citations

• Pullback and Pushout Constructions in C*-Algebra Theory

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