On a Counterexample to a Conjecture by Blackadar
Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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On a Counterexample to a Conjecture by Blackadar. / Sørensen, Adam Peder Wie.
Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012. red. / Toke M. Clausen; Søren Eilers; Gunnar Restorff; Sergei Silvestrov. Springer, 2013. s. 295-303 (Springer Proceedings in Mathematics & Statistics , Bind 58).Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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TY - GEN
T1 - On a Counterexample to a Conjecture by Blackadar
AU - Sørensen, Adam Peder Wie
PY - 2013
Y1 - 2013
N2 - Blackadar conjectured that if we have a split short-exact sequence 0→I→A→C→0 where I is semiprojective then A must be semiprojective. Eilers and Katsura have found a counterexample to this conjecture. Presumably Blackadar asked that the extension be split to make it more likely that semiprojectivity of I would imply semiprojectivity of A. But oddly enough, in all the counterexamples of Eilers and Katsura the quotient map from A to A/I≅C is split. We will show how to modify their examples to find a non-semiprojective C∗-algebra B with a semiprojective ideal J such that B∕J is the complex numbers and the quotient map does not split.
AB - Blackadar conjectured that if we have a split short-exact sequence 0→I→A→C→0 where I is semiprojective then A must be semiprojective. Eilers and Katsura have found a counterexample to this conjecture. Presumably Blackadar asked that the extension be split to make it more likely that semiprojectivity of I would imply semiprojectivity of A. But oddly enough, in all the counterexamples of Eilers and Katsura the quotient map from A to A/I≅C is split. We will show how to modify their examples to find a non-semiprojective C∗-algebra B with a semiprojective ideal J such that B∕J is the complex numbers and the quotient map does not split.
U2 - 10.1007/978-3-642-39459-1_15
DO - 10.1007/978-3-642-39459-1_15
M3 - Article in proceedings
SN - 9783642394584
T3 - Springer Proceedings in Mathematics & Statistics
SP - 295
EP - 303
BT - Operator Algebra and Dynamics
A2 - Clausen, Toke M.
A2 - Eilers, Søren
A2 - Restorff, Gunnar
A2 - Silvestrov, Sergei
PB - Springer
ER -
ID: 97160488