On a Counterexample to a Conjecture by Blackadar
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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.
Original language | English |
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Title of host publication | Operator Algebra and Dynamics : Nordforsk Network Closing Conference, Faroe Islands, May 2012 |
Editors | Toke M. Clausen, Søren Eilers, Gunnar Restorff, Sergei Silvestrov |
Publisher | Springer |
Publication date | 2013 |
Pages | 295-303 |
ISBN (Print) | 9783642394584 |
ISBN (Electronic) | 9783642394591 |
DOIs | |
Publication status | Published - 2013 |
Series | Springer Proceedings in Mathematics & Statistics |
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Volume | 58 |
ID: 97160488