On the Decomposition Theorems for C*-algebras

2019/05/28 by Chunlan Jiang, Jiang, Chunlan, Liangqing Li +3
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1905.12447

40 pages. arXiv admin note: substantial text overlap with arXiv:1607.07581

arxiv created 2019/05/28 · openalex publication_date 2019/05/28 · arxiv updated 2019/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Elliott dimension drop interval algebra is an important class among all C^*-algebras in the classification theory. Especially, they are building stones of AHD algebra and the latter contains all AH algebras with the ideal property of no dimension growth. In this paper, we will show two decomposition theorems related to the Elliott dimension drop interval algebra. Our results are key steps in classifying all AH algebras with the ideal property of no dimension growth.

Citations

• A classification of inductive limit C^*-algebras with ideal property

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• A Note On Subhomogeneous C*-Algebras
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