On a Counterexample to a Conjecture by Blackadar

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt

Standard

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

Harvard

Sørensen, APW 2013, On a Counterexample to a Conjecture by Blackadar. i TM Clausen, S Eilers, G Restorff & S Silvestrov (red), Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012. Springer, Springer Proceedings in Mathematics & Statistics , bind 58, s. 295-303. https://doi.org/10.1007/978-3-642-39459-1_15

APA

Sørensen, A. P. W. (2013). On a Counterexample to a Conjecture by Blackadar. I T. M. Clausen, S. Eilers, G. Restorff, & S. Silvestrov (red.), Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012 (s. 295-303). Springer. Springer Proceedings in Mathematics & Statistics Bind 58 https://doi.org/10.1007/978-3-642-39459-1_15

Vancouver

Sørensen APW. On a Counterexample to a Conjecture by Blackadar. I Clausen TM, Eilers S, Restorff G, Silvestrov S, red., Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012. Springer. 2013. s. 295-303. (Springer Proceedings in Mathematics & Statistics , Bind 58). https://doi.org/10.1007/978-3-642-39459-1_15

Author

Sørensen, Adam Peder Wie. / On a Counterexample to a Conjecture by Blackadar. 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).

Bibtex

@inproceedings{e983fd7c049e463db04cc2bc43740d1e,
title = "On a Counterexample to a Conjecture by Blackadar",
abstract = "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.",
author = "S{\o}rensen, {Adam Peder Wie}",
year = "2013",
doi = "10.1007/978-3-642-39459-1_15",
language = "English",
isbn = "9783642394584",
series = "Springer Proceedings in Mathematics & Statistics ",
pages = "295--303",
editor = "Clausen, {Toke M.} and Eilers, {S{\o}ren } and Restorff, {Gunnar } and Silvestrov, {Sergei }",
booktitle = "Operator Algebra and Dynamics",
publisher = "Springer",
address = "Switzerland",

}

RIS

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