A characterization of semiprojectivity for commutative C*-algebras

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Standard

A characterization of semiprojectivity for commutative C*-algebras. / Sørensen, Adam Peder Wie; Theil, Hannes.

I: Proceedings of the London Mathematical Society, Bind 105, Nr. 5, 2012, s. 1021-1046.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Sørensen, APW & Theil, H 2012, 'A characterization of semiprojectivity for commutative C*-algebras', Proceedings of the London Mathematical Society, bind 105, nr. 5, s. 1021-1046. https://doi.org/10.1112/plms/pdr051

APA

Sørensen, A. P. W., & Theil, H. (2012). A characterization of semiprojectivity for commutative C*-algebras. Proceedings of the London Mathematical Society, 105(5), 1021-1046. https://doi.org/10.1112/plms/pdr051

Vancouver

Sørensen APW, Theil H. A characterization of semiprojectivity for commutative C*-algebras. Proceedings of the London Mathematical Society. 2012;105(5):1021-1046. https://doi.org/10.1112/plms/pdr051

Author

Sørensen, Adam Peder Wie ; Theil, Hannes. / A characterization of semiprojectivity for commutative C*-algebras. I: Proceedings of the London Mathematical Society. 2012 ; Bind 105, Nr. 5. s. 1021-1046.

Bibtex

@article{a371d6420d234391ab6f6d40eb70e687,
title = "A characterization of semiprojectivity for commutative C*-algebras",
abstract = "Given a compact metric space X, we show that the commutative C*-algebra C(X) is semiprojective if and only if X is an absolute neighbourhood retract of dimension at most 1. This confirms a conjecture of Blackadar. Generalizing to the non-unital setting, we derive a characterization of semiprojectivity for separable, commutative C*-algebras. As applications of our results, we prove two theorems about the structure of semiprojective commutative C*-algebras. Letting A be a commutative C*-algebra, we show firstly: If I is an ideal of A and A/I is finite-dimensional, then A is semiprojective if and only if I is; and secondly: A is semiprojective if and only if M2(A) is. This answers two questions about semiprojective C*-algebras in the commutative case. ",
author = "S{\o}rensen, {Adam Peder Wie} and Hannes Theil",
year = "2012",
doi = "10.1112/plms/pdr051",
language = "English",
volume = "105",
pages = "1021--1046",
journal = "Proceedings of the London Mathematical Society",
issn = "0024-6115",
publisher = "Oxford University Press",
number = "5",

}

RIS

TY - JOUR

T1 - A characterization of semiprojectivity for commutative C*-algebras

AU - Sørensen, Adam Peder Wie

AU - Theil, Hannes

PY - 2012

Y1 - 2012

N2 - Given a compact metric space X, we show that the commutative C*-algebra C(X) is semiprojective if and only if X is an absolute neighbourhood retract of dimension at most 1. This confirms a conjecture of Blackadar. Generalizing to the non-unital setting, we derive a characterization of semiprojectivity for separable, commutative C*-algebras. As applications of our results, we prove two theorems about the structure of semiprojective commutative C*-algebras. Letting A be a commutative C*-algebra, we show firstly: If I is an ideal of A and A/I is finite-dimensional, then A is semiprojective if and only if I is; and secondly: A is semiprojective if and only if M2(A) is. This answers two questions about semiprojective C*-algebras in the commutative case.

AB - Given a compact metric space X, we show that the commutative C*-algebra C(X) is semiprojective if and only if X is an absolute neighbourhood retract of dimension at most 1. This confirms a conjecture of Blackadar. Generalizing to the non-unital setting, we derive a characterization of semiprojectivity for separable, commutative C*-algebras. As applications of our results, we prove two theorems about the structure of semiprojective commutative C*-algebras. Letting A be a commutative C*-algebra, we show firstly: If I is an ideal of A and A/I is finite-dimensional, then A is semiprojective if and only if I is; and secondly: A is semiprojective if and only if M2(A) is. This answers two questions about semiprojective C*-algebras in the commutative case.

U2 - 10.1112/plms/pdr051

DO - 10.1112/plms/pdr051

M3 - Journal article

VL - 105

SP - 1021

EP - 1046

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 5

ER -

ID: 49471201