A characterization of semiprojectivity for commutative C*-algebras
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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
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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