The ideal structure of the Haagerup tensor product of C*-algebras.

1993 ◽  
Vol 1993 (442) ◽  
pp. 111-148
Keyword(s):  
Tensor Product ◽  
Ideal Structure ◽  
C Algebras ◽  
The Ideal

Noetherian Tensor Products

1972 ◽  
Vol 15 (2) ◽  
pp. 235-238
Author(s):  
E. A. Magarian ◽  
J. L. Motto
Keyword(s):  
Tensor Product ◽  
Jacobson Radical ◽  
Tensor Products ◽  
Minimum Condition ◽  
Ideal Structure ◽  
The Ideal

Relatively little is known about the ideal structure of A⊗RA' when A and A' are R-algebras. In [4, p. 460], Curtis and Reiner gave conditions that imply certain tensor products are semi-simple with minimum condition. Herstein considered when the tensor product has zero Jacobson radical in [6, p. 43]. Jacobson [7, p. 114] studied tensor products with no two-sided ideals, and Rosenberg and Zelinsky investigated semi-primary tensor products in [9].All rings considered in this paper are assumed to be commutative with identity. Furthermore, R will always denote a field.

scholarly journals Condition (K) for inverse semigroups and the ideal structure of their C⁎-algebras

2019 ◽  
Vol 523 ◽  
pp. 119-153 ◽  
Author(s):  
Scott M. LaLonde ◽  
David Milan ◽  
Jamie Scott
Keyword(s):  
Inverse Semigroups ◽  
Ideal Structure ◽  
C Algebras ◽  
The Ideal

scholarly journals Exel's crossed product for non-unital C*-algebras

2010 ◽  
Vol 149 (3) ◽  
pp. 423-444 ◽  
Author(s):  
NATHAN BROWNLOWE ◽  
IAIN RAEBURN ◽  
SEAN T. VITTADELLO
Keyword(s):  
Dynamical Systems ◽  
Transfer Operator ◽  
Finite Graph ◽  
Crossed Product ◽  
Crossed Products ◽  
Ideal Structure ◽  
Locally Finite ◽  
C Algebras ◽  
Locally Finite Graph ◽  
The Ideal

AbstractWe consider a family of dynamical systems (A, α, L) in which α is an endomorphism of a C*-algebra A and L is a transfer operator for α. We extend Exel's construction of a crossed product to cover non-unital algebras A, and show that the C*-algebra of a locally finite graph can be realised as one of these crossed products. When A is commutative, we find criteria for the simplicity of the crossed product, and analyse the ideal structure of the crossed product.

Spectra for Infinite Tensor Product Type Actions of Compact Groups

1996 ◽  
Vol 48 (2) ◽  
pp. 330-342
Author(s):  
Elliot C. Gootman ◽  
Aldo J. Lazar
Keyword(s):  
Tensor Product ◽  
Compact Group ◽  
Abelian Groups ◽  
Product Type ◽  
Crossed Product ◽  
Compact Groups ◽  
Ideal Structure ◽  
Crossed Product Algebra ◽  
Product Algebra ◽  
The Ideal

AbstractWe present explicit calculations of the Arveson spectrum, the strong Arveson spectrum, the Connes spectrum, and the strong Connes spectrum, for an infinite tensor product type action of a compact group. Using these calculations and earlier results (of the authors and C. Peligrad) relating the various spectra to the ideal structure of the crossed product algebra, we prove that the topology of G influences the ideal structure of the crossed product algebra, in the following sense: if G contains a nontrivial connected group as a direct summand, then the crossed product algebra may be prime, but it is never simple; while if G is discrete, the crossed product algebra is simple if and only if it is prime. These results extend to compact groups analogous results of Bratteli for abelian groups. In addition, we exhibit a class of examples illustrating that for compact groups, unlike the case for abelian groups, the Connes spectrum and strong Connes spectrum need not be stable.

scholarly journals Nontrivially Noetherian $C^*$-algebras

2012 ◽  
Vol 111 (1) ◽  
pp. 135 ◽  
Author(s):  
Taylor Hines ◽  
Erik Walsberg
Keyword(s):  
Chain Condition ◽  
Ideal Structure ◽  
C Algebra ◽  
C Algebras ◽  
Finite Dimensional ◽  
Primitive Ideals ◽  
Descending Chain Condition ◽  
Ascending Chain Condition ◽  
The Ideal

We say that a $C^*$-algebra is Noetherian if it satisfies the ascending chain condition for two-sided closed ideals. A nontrivially Noetherian $C^*$-algebra is one with infinitely many ideals. Here, we show that nontrivially Noetherian $C^*$-algebras exist, and that a separable $C^*$-algebra is Noetherian if and only if it contains countably many ideals and has no infinite strictly ascending chain of primitive ideals. Furthermore, we prove that every Noetherian $C^*$-algebra has a finite-dimensional center. Where possible, we extend results about the ideal structure of $C^*$-algebras to Artinian $C^*$-algebras (those satisfying the descending chain condition for closed ideals).

scholarly journals Nuclear subalgebras of UHF C*-algebras

1986 ◽  
Vol 29 (1) ◽  
pp. 97-100 ◽  
Author(s):  
R. J. Archbold ◽  
Alexander Kumjian
Keyword(s):  
Tensor Product ◽  
Inductive Limit ◽  
Inductive Limits ◽  
C Algebra ◽  
C Algebras ◽  
Finite Dimensional ◽  
The Family ◽  
Algebraic Tensor Product

A C*-algebra A is said to be approximately finite dimensional (AF) if it is the inductive limit of a sequence of finite dimensional C*-algebras(see [2], [5]). It is said to be nuclear if, for each C*-algebra B, there is a unique C*-norm on the *-algebraic tensor product A ⊗B [11]. Since finite dimensional C*-algebras are nuclear, and inductive limits of nuclear C*-algebras are nuclear [16];,every AF C*-algebra is nuclear. The family of nuclear C*-algebras is a large and well-behaved class (see [12]). The AF C*-algebras for a particularly tractable sub-class which has been completely classified in terms of the invariant K0 [7], [5].

The ideal structure of XX

1984 ◽  
Vol 30 (1) ◽  
pp. 41-51 ◽  
Author(s):  
Neil Hindman ◽  
Paul Milnes
Keyword(s):  
Ideal Structure ◽  
The Ideal

scholarly journals Falling -Ideals in -Algebras

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Young Bae Jun ◽  
Sun Shin Ahn ◽  
Kyoung Ja Lee
Keyword(s):  
Theoretical Approach ◽  
Ideal Structure ◽  
Fundamental Properties ◽  
The Ideal

Based on the theory of a falling shadow which was first formulated by Wang (1985), a theoretical approach of the ideal structure in -algebras is established. The notions of a falling -subalgebra, a falling -ideal, a falling -ideal, and a falling -ideal of a -algebra are introduced. Some fundamental properties are investigated. Relations among a falling -subalgebra, a falling -ideal, a falling -ideal, and a falling -ideal are stated. Characterizations of falling -ideals and falling -ideals are discussed. A relation between a fuzzy -subalgebra and a falling -subalgebra is provided.

scholarly journals The ideal structure of the Hecke $C^*$ -algebra of Bost and Connes

2000 ◽  
Vol 318 (3) ◽  
pp. 433-451 ◽  
Author(s):  
Marcelo Laca ◽  
Iain Raeburn
Keyword(s):  
Ideal Structure ◽  
C Algebra ◽  
The Ideal
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