Homotopy classification of projections in the corona algebra of a non-simple $C\sp *$-algebra

Details Homotopy classification of projections in the corona algebra of a non-simple $C\sp *$-algebra Homotopy classification of projections in the corona algebra of a non-simple $C\sp *$-algebra

2010-10-10

arxiv.org/abs/1010.1936v1

Mathematics

Operator Algebras

32 pages, announced in GPOTS2008

Scientific paper

We study projections in the corona algebra of $C(X)\otimes K$ where $X=[0,1],[0,\infty),(-\infty,\infty)$, and $[0,1]/\{0,1 \}$. 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. Then we also characterize the conditions for two projections to be equal in $K_0$-group, Murray-von Neumann equivalent, unitarily equivalent, and homotopic from the weakest to the strongest. In light of these characterizations, we construct examples showing that any two equivalence notions do not coincide, which serve as examples of non-stable K-theory of $C\sp*$-algebras.

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