TY - GEN
T1 - Graph C*-algebras with a T1 primitive ideal space
AU - Gabe, J.
PY - 2013
Y1 - 2013
N2 - We give necessary and sufficient conditions which a graph should satisfy in order for its associated C
*-algebra to have a T
1 primitive ideal space. We give a description of which one-point sets in such a primitive ideal space are open, and use this to prove that any purely infinite graph C
*-algebrapurely infinite graph C
*-algebra purely infinite graph C
*-algebra with a T
1 (in particular Hausdorff) primitive ideal space, is a c
0-direct sum of Kirchberg algebra. Moreover, we show that graph C
*-algebras with a T
1 primitive ideal space canonically may be given the structure of a C(ℕ̃)-algebra, and that isomorphisms of their ℕ̃-filtered K-theory (without coefficients) lift to E(ℕ̃)-equivalences, as defined by Dadarlat and Meyer.
AB - We give necessary and sufficient conditions which a graph should satisfy in order for its associated C
*-algebra to have a T
1 primitive ideal space. We give a description of which one-point sets in such a primitive ideal space are open, and use this to prove that any purely infinite graph C
*-algebrapurely infinite graph C
*-algebra purely infinite graph C
*-algebra with a T
1 (in particular Hausdorff) primitive ideal space, is a c
0-direct sum of Kirchberg algebra. Moreover, we show that graph C
*-algebras with a T
1 primitive ideal space canonically may be given the structure of a C(ℕ̃)-algebra, and that isomorphisms of their ℕ̃-filtered K-theory (without coefficients) lift to E(ℕ̃)-equivalences, as defined by Dadarlat and Meyer.
KW - Filtered K-theory
KW - Primitive ideal space
U2 - 10.1007/978-3-642-39459-1__7
DO - 10.1007/978-3-642-39459-1__7
M3 - Article in proceedings
SN - 9783642394584
T3 - Springer Proceedings in Mathematics & Statistics
SP - 141
EP - 156
BT - Operator Algebra and Dynamics - Nordforsk Network Closing Conference
PB - Springer
Y2 - 15 May 2012 through 20 May 2012
ER -