Irreducible Representations of the C ∗ -Algebra Generated by an n-Normal Operator

1972 ◽  
Vol 171 ◽  
pp. 301 ◽  
Author(s):  
John W. Bunce ◽  
James A. Deddens
Keyword(s):  
Normal Operator ◽  
Irreducible Representations ◽  
C Algebra

On the “Third Definition” of the Topology on the Spectrum of a C*-Algebra

1971 ◽  
Vol 23 (3) ◽  
pp. 445-450 ◽  
Author(s):  
L. Terrell Gardner
Keyword(s):  
Hilbert Space ◽  
Quotient Space ◽  
Principal Result ◽  
Irreducible Representations ◽  
C Algebra ◽  
Fell Topology ◽  
The Third ◽  
Definition Of ◽  
Image Position

0. In [3], Fell introduced a topology on Rep (A,H), the collection of all non-null but possibly degenerate *-representations of the C*-algebra A on the Hilbert space H. This topology, which we will call the Fell topology, can be described by giving, as basic open neighbourhoods of π0 ∈ Rep(A, H), sets of the formwhere the ai ∈ A, and the ξj ∈ H(π0), the essential space of π0 [4].A principal result of [3, Theorem 3.1] is that if the Hilbert dimension of H is large enough to admit all irreducible representations of A, then the quotient space Irr(A, H)/∼ can be identified with the spectrum (or “dual“) Â of A, in its hull-kernel topology.

scholarly journals Finitely generated nilpotent group C*-algebras have finite nuclear dimension

2018 ◽  
Vol 2018 (738) ◽  
pp. 281-298 ◽  
Author(s):  
Caleb Eckhardt ◽  
Paul McKenney
Keyword(s):  
Irreducible Representation ◽  
Nilpotent Group ◽  
Nilpotent Groups ◽  
Irreducible Representations ◽  
Finitely Generated ◽  
C Algebra ◽  
C Algebras ◽  
K Theory ◽  
Universal Coefficient Theorem ◽  
Torsion Free

Abstract We show that group C*-algebras of finitely generated, nilpotent groups have finite nuclear dimension. It then follows, from a string of deep results, that the C*-algebra A generated by an irreducible representation of such a group has decomposition rank at most 3. If, in addition, A satisfies the universal coefficient theorem, another string of deep results shows it is classifiable by its ordered K-theory and is approximately subhomogeneous. We observe that all C*-algebras generated by faithful irreducible representations of finitely generated, torsion free nilpotent groups satisfy the universal coefficient theorem.

QUANTIZATION AND SUPERSELECTION SECTORS I: TRANSFORMATION GROUP C*-ALGEBRAS

1990 ◽  
Vol 02 (01) ◽  
pp. 45-72 ◽  
Author(s):  
N.P. LANDSMAN
Keyword(s):  
Irreducible Representation ◽  
Large Class ◽  
Configuration Space ◽  
Topological Charge ◽  
Transformation Group ◽  
Irreducible Representations ◽  
Locally Compact ◽  
C Algebra ◽  
C Algebras ◽  
Charge Quantization

Quantization is defined as the act of assigning an appropriate C*-algebra [Formula: see text] to a given configuration space Q, along with a prescription mapping self-adjoint elements of [Formula: see text] into physically interpretable observables. This procedure is adopted to solve the problem of quantizing a particle moving on a homogeneous locally compact configuration space Q=G/H. Here [Formula: see text] is chosen to be the transformation group C*-algebra corresponding to the canonical action of G on Q. The structure of these algebras and their representations are examined in some detail. Inequivalent quantizations are identified with inequivalent irreducible representations of the C*-algebra corresponding to the system, hence with its superselection sectors. Introducing the concept of a pre-Hamiltonian, we construct a large class of G-invariant time-evolutions on these algebras, and find the Hamiltonians implementing these time-evolutions in each irreducible representation of [Formula: see text]. “Topological” terms in the Hamiltonian (or the corresponding action) turn out to be representation-dependent, and are automatically induced by the quantization procedure. Known “topological” charge quantization or periodicity conditions are then identically satisfied as a consequence of the representation theory of [Formula: see text].

CORE SYMMETRIES OF A FLOW

2004 ◽  
Vol 16 (04) ◽  
pp. 479-507
Author(s):  
AKITAKA KISHIMOTO
Keyword(s):  
Equivalence Classes ◽  
Crossed Product ◽  
Irreducible Representations ◽  
Group Of Automorphisms ◽  
C Algebra ◽  
Kms State ◽  
Cocycle Perturbation

For a flow α on a C*-algebra one defines a symmetry as the group of automorphisms γ such that γαγ-1 is a cocycle perturbation of α. We propose to define a core of this symmetry, which acts trivially on the set of equivalence classes of KMS state representations, but may act non-trivially on the set of equivalence classes of covariant irreducible representations. In particular this core acts transitively on the set of those which induce faithful representations of the crossed product by α.

scholarly journals The coordinate algebra of a quantum symplectic sphere does not embed into any C*-algebra

2021 ◽  
pp. 1-11
Author(s):  
Francesco D’Andrea ◽  
Giovanni Landi
Keyword(s):  
Irreducible Representations ◽  
C Algebra ◽  
Coordinate Algebra ◽  
Bounded Representation

In this note, we generalize a result of Mikkelsen–Szymański and show that, for every [Formula: see text], any bounded ∗-representation of the quantum symplectic sphere [Formula: see text] annihilates the first [Formula: see text] generators. We then classify irreducible representations of its coordinate algebra [Formula: see text].

scholarly journals CENTRAL SEQUENCES IN SUBHOMOGENEOUS UNITAL C*-ALGEBRAS

2020 ◽  
pp. 1-8
Author(s):  
DON HADWIN ◽  
HEMANT PENDHARKAR
Keyword(s):  
Irreducible Representations ◽  
C Algebra ◽  
Central Sequence ◽  
C Algebras ◽  
Pointwise Limit ◽  
Central Sequences ◽  
Multiplicity Free

Abstract Suppose that $\mathcal {A}$ is a unital subhomogeneous C*-algebra. We show that every central sequence in $\mathcal {A}$ is hypercentral if and only if every pointwise limit of a sequence of irreducible representations is multiplicity free. We also show that every central sequence in $\mathcal {A}$ is trivial if and only if every pointwise limit of irreducible representations is irreducible. Finally, we give a nice representation of the latter algebras.

ALMOST NORMAL ELEMENTS

1994 ◽  
Vol 05 (05) ◽  
pp. 765-778 ◽  
Author(s):  
HUAXIN LIN
Keyword(s):  
Normal Operator ◽  
Diagonal Block ◽  
Spectral Condition ◽  
Diagonal Operator ◽  
Finite Spectrum ◽  
C Algebra ◽  
Finite Matrix ◽  
Normal Element ◽  
Block Diagonal

We show that, for any ε > 0, there exists δ > 0, such that for any finite matrix T with ||T|| ≤ 1 satisfies [Formula: see text] there is a normal operator N ∈ B (l2) such that [Formula: see text] where T∞ is the block diagonal operator with T on each diagonal block. We also show that, for any ε > 0, there exists δ > 0 such that for any element x with ||x|| ≤ 1 in any purely infinite simple C*-algebra A satisfies [Formula: see text] and a spectral condition, there is a normal element y ∈ A with finite spectrum [Formula: see text]

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