- March 4, 2011, Friday - 15h00 (Room P
3.10):
N. Christopher Phillips
(University of Oregon, USA)
" Equivariant
semiprojectivity and applications "
Abstract. A C*-algebra
A is semiprojective if, roughly speaking, any approximate homomorphism
from A to some other C*-algebra is close to an actual homomorphism.
(There are several different ways to make this precise, leading to
several different concepts.) There are not very many semiprojective
C*-algebras, but the ones that do exist (and the fact that they are
semiprojective) play an important role in the theory. Examples of
semiprojective C*-algebras include finite dimensional C*-algebras, the
algebra of continuous functions from the interval or circle to a finite
dimensional C*-algebra, the Cuntz algebras and some of their
generalizations, and the full C*-algebras of free groups.
Now suppose that a compact group G acts on A. We say that A is
equivariantly semiprojective if, roughly speaking, whenever B is
another C*-algebra with an action of G, then every approximately
equivariant approximate homomorphism from A to B is close to an exactly
equivariant homomorphism. We prove that finite dimensional C*-algebras
are equivariantly semiprojective, as well as Cuntz algebras with
certain special actions.
One of the many applications of semiprojectivity is to classification
theorems. In the classification of purely infinite simple C*-algebras,
semiprojectivity is used to replace asymptotic morphisms with
homomorphisms. We expect equivariant semiprojectivity to play the same
role in the classification of actions of compact groups on purely
infinite simple C*-algebras.
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