On a counterexample to a conjecture by blackadar

Authors

Adam P. Sorensen, University of WollongongFollow

RIS ID

88033

Publication Details

Sorensen, A. P. W. (2013). On a counterexample to a conjecture by blackadar. Springer Proceedings in Mathematics & Statistics, 58 295-303.

Abstract

Blackadar conjectured that if we have a split short-exact sequence 0-I-A-C-0 were 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 idal J such that B/J is the complex numbers and the quotient map does not split.