scholarly journals Jacobson topology of the primitive ideal space of self-similar k-graph C*-algebras

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
Hui Li
Keyword(s):  
Primitive Ideal ◽  
Ideal Space ◽  
C Algebras ◽  
Self Similar

Ideal Spaces of the Haagerup Tensor Product of C*-Algebras

1997 ◽  
Vol 08 (01) ◽  
pp. 1-29 ◽  
Author(s):  
Robert J. Archbold ◽  
Douglas W. B. Somerset ◽  
Eberhard Kaniuth ◽  
Günter Schlichting
Keyword(s):  
Tensor Product ◽  
Primitive Ideal ◽  
Ideal Space ◽  
C Algebras

Following the work of Allen, Sinclair and Smith on the primitive ideal space of the Haagerup tensor product A ⊗ hB of C*-algebras A and B, we investigate the hull-kernel topology and use this to determine various other ideal spaces and their topologies in relation to the corresponding ideal spaces of A and B. We study the semi-continuity of norm functions I → ||x + I||(x ∈ A ⊗h B) on these ideal spaces and identify the separated points of Prim (A ⊗h B). Finally, we exhibit several conditions each of which is equivalent to the quasi-standardness of A ⊗h B.

Minimal primal ideal spaces and norms of inner derivations of tensor products of C*-algebras

1996 ◽  
Vol 119 (2) ◽  
pp. 297-308 ◽  
Author(s):  
Eberhard Kaniuth
Keyword(s):  
Cross Sections ◽  
Dense Subset ◽  
Tensor Products ◽  
The Other ◽  
Primitive Ideal ◽  
Ideal Space ◽  
C Algebra ◽  
C Algebras ◽  
Other Hand ◽  
Full Algebra

An ideal I in a C*-algebra A is called primal if whenever n ≥ 2 and J1,…, Jn are ideals in A with zero product then Jk ⊆ I for at least one k. The topologized space of minimal primal ideals of A, Min-Primal (A), has been extensively studied by Archbold[3]. Very much in the spirit of Fell's work [14] it was shown in [3, theorem 5·3] (see also [5, theorem 3·4]) that if A is quasi-standard, then A is *-isomorphic to a maximal full algebra of cross-sections of Min-Primal (A). Moreover, if A is separable the fibre algebras are primitive throughout a dense subset. On the other hand, the complete regularization of the primitive ideal space of A gives rise to the space of so-called Glimm ideals of A, Glimm (A). It turned out that A is quasi-standard exactly when Min-Primal (A) and Glimm (A) coincide as sets and topologically [5, theorem 3·3].

scholarly journals Some groups with T1 primitive ideal spaces

1985 ◽  
Vol 38 (1) ◽  
pp. 55-64 ◽  
Author(s):  
A. L. Carey ◽  
W. Moran
Keyword(s):  
Normal Subgroup ◽  
Lie Groups ◽  
Lie Group ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Solvable Lie Groups ◽  
Locally Compact ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet G be a second countable locally compact group possessing a normal subgroup N with G/N abelian. We prove that if G/N is discrete then G has T1 primitive ideal space if and only if the G-quasiorbits in Prim N are closed. This condition on G-quasiorbits arose in Pukanzky's work on connected and simply connected solvable Lie groups where it is equivalent to the condition of Auslander and Moore that G be type R on N (-nilradical). Using an abstract version of Pukanzky's arguments due to Green and Pedersen we establish that if G is a connected and simply connected Lie group then Prim G is T1 whenever G-quasiorbits in [G, G] are closed.

scholarly journals Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras

2014 ◽  
Vol 14 (3) ◽  
pp. 570-613 ◽  
Author(s):  
Sara E. Arklint ◽  
Rasmus Bentmann ◽  
Takeshi Katsura
Keyword(s):  
Primitive Ideal ◽  
Ideal Space ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
K Theory

AbstractWe show that filtered K-theory is equivalent to a substantially smaller invariant for all real-rank-zero C*-algebras with certain primitive ideal spaces—including the infinitely many so-called accordion spaces for which filtered K-theory is known to be a complete invariant. As a consequence, we give a characterization of purely infinite Cuntz–Krieger algebras whose primitive ideal space is an accordion space.

Quasi-standard C*-algebras

1990 ◽  
Vol 107 (2) ◽  
pp. 349-360 ◽  
Author(s):  
R. J. Archbold ◽  
D. W. B. Somerset
Keyword(s):  
Cross Sections ◽  
Equivalence Relation ◽  
Dense Subset ◽  
Base Space ◽  
Ideal Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
C Algebras ◽  
Necessary And Sufficient ◽  
Full Algebra

AbstactA necessary and sufficient condition is given for a separable C*-algebra to be *-isomorphic to a maximal full algebra of cross-sections over a base space such that the fibre algebras are primitive throughout a dense subset. The condition is that the relation of inseparability for pairs of points in the primitive ideal space should be an open equivalence relation.

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