Graph C*-Algebras with a T1 Primitive Ideal Space
Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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Graph C*-Algebras with a T1 Primitive Ideal Space. / Gabe, James 'Jamie'.
Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012. red. / Toke M. Clausen; Søren Eilers; Gunnar Restorff; Sergei Silvestrov. Springer, 2013. s. 141-156 (Springer Proceedings in Mathematics & Statistics , Bind 58).Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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TY - GEN
T1 - Graph C*-Algebras with a T1 Primitive Ideal Space
AU - Gabe, James 'Jamie'
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 T1 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 anypurely infinite graph C∗-algebrapurely infinite graph C∗-algebra purely infinite graph C∗-algebra with a T1 (in particular Hausdorff) primitive ideal space, is a c0-direct sum of Kirchberg algebras. Moreover, we show that graph C∗-algebras with a T1 primitive ideal space canonically may be given the structure of a C(N ~ ) -algebra, and that isomorphisms of their N ~ -filtered K-theory (without coefficients) lift to E(N ~ ) -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 T1 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 anypurely infinite graph C∗-algebrapurely infinite graph C∗-algebra purely infinite graph C∗-algebra with a T1 (in particular Hausdorff) primitive ideal space, is a c0-direct sum of Kirchberg algebras. Moreover, we show that graph C∗-algebras with a T1 primitive ideal space canonically may be given the structure of a C(N ~ ) -algebra, and that isomorphisms of their N ~ -filtered K-theory (without coefficients) lift to E(N ~ ) -equivalences, as defined by Dadarlat and Meyer
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
A2 - Clausen, Toke M.
A2 - Eilers, Søren
A2 - Restorff, Gunnar
A2 - Silvestrov, Sergei
PB - Springer
ER -
ID: 97157824