21,054 research outputs found
On a counterexample to a conjecture by Blackadar
Blackadar conjectured that if we have a split short-exact sequence 0 -> I ->
A -> A/I -> 0 where I is semiprojective and A/I is isomorphic to the complex
numbers, 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 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.Comment: 6 page
- …