Krull dimension for C*-algebras-Reference-Cited by-同舟云学术

Krull dimension for C*-algebras

Published:2022-07-23 Issue:0 Volume:0 Page:
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Rouzbehani Mohammad¹^ORCID,Amini Massoud²^ORCID,Asadi Mohammad B.¹

Affiliation:

1. School of Mathematics, Statistics and Computer Science , College of Science , University of Tehran , Tehran , Iran

2. Department of Mathematics , Faculty of Mathematical Sciences , Tarbiat Modares University ; and School of Mathematics, Institute for Research in Fundamental Sciences (IPM) , Tehran 19395-5746 , Iran

Abstract

Abstract In this article, we introduce and study the notion of Krull dimension for C*-algebras. We show that every C*-algebra with Krull dimension contains an essential ideal that is a finite direct sum of critical ideals. We show that a C*-algebra with Krull dimension has finite-dimensional center, and conclude that every graph C*-algebra with Krull dimension has real rank zero, and is 𝒪 ∞

{\mathcal{O}_{\infty}}

-stable in the purely infinite case. We also study the (weak) ideal property for critical C*-algebras.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2021-0304/pdf

Reference38 articles.

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3. G. Aranda Pino, F. Perera and M. Siles Molina, Graph Algebras: Bridging the Gap Between Analysis and Algebra, University of Málaga, Málaga, Spain, 2007.

4. W. Beer, On Morita equivalence of nuclear C ∗ C^{\ast} -algebras, J. Pure Appl. Algebra 26 (1982), no. 3, 249–267.

5. B. Blackadar, Operator Algebras. Theory of C * C^{*} -Algebras and von Neumann Algebras, Encyclopaedia Math. Sci. 122, Springer, Berlin, 2006.

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