1 results
Homotopy Classification of Projections in the Corona Algebra of a Non-simple C*-algebra
-
- Journal:
- Canadian Journal of Mathematics / Volume 64 / Issue 4 / 01 August 2012
- Published online by Cambridge University Press:
- 20 November 2018, pp. 755-777
- Print publication:
- 01 August 2012
-
- Article
-
- You have access
- Export citation
-
We study projections in the corona algebra of
$C\left( X \right)\,\otimes \,K$, where 
$K$ is the 
${{C}^{*}}$-algebra of compact operators on a separable infinite dimensional Hilbert space and 
$X\,=\,[0,\,1],\,[0,\,\infty ),\,(-\infty ,\,\infty ),\,\text{or}\,\text{ }\!\![\!\!\text{ 0,}\,\text{1 }\!\!]\!\!\text{ / }\!\!\{\!\!\text{ 0,}\,\text{1 }\!\!\}\!\!\text{ }$. Using BDF's essential codimension, we determine conditions for a projection in the corona algebra to be liftable to a projection in the multiplier algebra. We also determine the conditions for two projections to be equal in 
${{K}_{0}}$, Murray-von Neumann equivalent, unitarily equivalent, or homotopic. In light of these characterizations, we construct examples showing that the equivalence notions above are all distinct.
