On the extension of unitary group isomorphisms of unital UHF-algebras

2015 ◽  
Vol 26 (08) ◽  
pp. 1550061
Author(s):  
Ahmed Al-Rawashdeh
Keyword(s):  
Large Class ◽  
Unitary Group ◽  
Unitary Groups ◽  
Type I ◽  
Linear Isomorphism ◽  
Linear Automorphism ◽  
C Algebras ◽  
Two Factors ◽  
Continuous Automorphism

H. Dye showed that an isomorphism between the (discrete) unitary groups in two factors not of type In is implemented by a linear (or a conjugate linear) *-isomorphism of the factors. If φ is an isomorphism between the unitary groups of two unital C*-algebras, it induces a bijective map θφ between the sets of projections. For certain UHF-algebras, we construct an automorphism φ of their unitary group, such that θφ does not preserve the orthogonality of projections. For a large class of unital finite C*-algebras, we show that θφ is always an orthoisomorphism. If φ is a continuous automorphism of the unitary group of a UHF-algebra A, we show that φ is implemented by a linear or a conjugate linear *-automorphism of A.

APPROXIMATELY INNER FLOWS ON SEPARABLE C*-ALGEBRAS

2002 ◽  
Vol 14 (07n08) ◽  
pp. 649-673 ◽  
Author(s):  
AKITAKA KISHIMOTO
Keyword(s):  
Irreducible Representation ◽  
Von Neumann Algebra ◽  
Automorphism Groups ◽  
Unitary Groups ◽  
Type I ◽  
Von Neumann ◽  
C Algebra ◽  
C Algebras ◽  
Inner Automorphism ◽  
Uniformly Continuous

We present two types of result for approximately inner one-parameter automorphism groups (referred to as AI flows hereafter) of separable C*-algebras. First, if there is an irreducible representation π of a separable C*-algebra A such that π(A) does not contain non-zero compact operators, then there is an AI flow α such that π is α-covariant and α is far from uniformly continuous in the sense that α induces a flow on π(A) which has full Connes spectrum. Second, if α is an AI flow on a separable C*-algebra A and π is an α-covariant irreducible representation, then we can choose a sequence (hn) of self-adjoint elements in A such that αt is the limit of inner flows Ad eithn and the sequence π(eithn) of one-parameter unitary groups (referred to as unitary flows hereafter) converges to a unitary flow which implements α in π. This latter result will be extended to cover the case of weakly inner type I representations. In passing we shall also show that if two representations of a separable simple C*-algebra on a separable Hilbert space generate the same von Neumann algebra of type I, then there is an approximately inner automorphism which sends one into the other up to equivalence.

Structure and regulation of the human interferon regulatory factor 1 (IRF-1) and IRF-2 genes: implications for a gene network in the interferon system

1994 ◽  
Vol 14 (2) ◽  
pp. 1500-1509
Author(s):  
H Harada ◽  
E Takahashi ◽  
S Itoh ◽  
K Harada ◽  
T A Hori ◽  
...  
Keyword(s):  
Gene Network ◽  
Interferon Regulatory Factor ◽  
Chromosomal Mapping ◽  
Human Interferon ◽  
Type I ◽  
Regulatory Factor ◽  
Nf Kappa B ◽  
Interferon Regulatory Factor 1 ◽  
Two Factors ◽  
Dna Binding Factors

Interferon regulatory factor 1 (IRF-1) and IRF-2 are structurally similar DNA-binding factors which were originally identified as regulators of the type I interferon (IFN) system; the former functions as a transcriptional activator, and the latter represses IRF-1 function by competing for the same cis elements. More recent studies have revealed new roles of the two factors in the regulation of cell growth; IRF-1 and IRF-2 manifest antioncogenic and oncogenic activities, respectively. In this study, we determined the structures and chromosomal locations of the human IRF-1 and IRF-2 genes and further characterized the promoters of the respective genes. Comparison of exon-intron organization of the two genes revealed a common evolutionary structure, notably within the exons encoding the N-terminal portions of the two factors. We confirmed the chromosomal mapping of the human IRF-1 gene to 5q31.1 and newly assigned the IRF-2 gene to 4q35.1, using fluorescence in situ hybridization. The 5' regulatory regions of both genes contain highly GC-rich sequences and consensus binding sequences for several known transcription factors, including NF-kappa B. Interestingly, one IRF binding site was found within the IRF-2 promoter, and expression of the IRF-2 gene was affected by both transient and stable IRF-1 expression. In addition, one potential IFN-gamma-activated sequence was found within the IRF-1 promoter. Thus, these results may shed light on the complex gene network involved in regulation of the IFN system.

scholarly journals C*–algebras Nearly Contained in Type I Algebras

2013 ◽  
Vol 65 (1) ◽  
pp. 52-65
Author(s):  
Erik Christensen ◽  
Allan M. Sinclair ◽  
Roger R. Smith ◽  
Stuart White
Keyword(s):  
Type I ◽  
C Algebras ◽  
Similarity Problem

AbstractIn this paper we consider near inclusions of C*-algebras. We show that if B is a separable type I C*-algebra and A satisfies Kadison's similarity problem, then A is also type I. We then use this to obtain an embedding of A into B.

scholarly journals Fast Constructive Recognition of Black-Box Unitary Groups

2003 ◽  
Vol 6 ◽  
pp. 162-197 ◽  
Author(s):  
Peter A. Brooksbank
Keyword(s):  
Homomorphic Image ◽  
Polynomial Time ◽  
Unitary Group ◽  
Black Box ◽  
Unitary Groups ◽  
Discrete Logarithms ◽  
Cyclic Groups

AbstractIn this paper, the author presents a new algorithm to recognise, constructively, when a given black-box group is a homomorphic image of the unitary group SU(d, q) for known d and q. The algorithm runs in polynomial time, assuming the existence of oracles for handling SL(2, q) subgroups, and for computing discrete logarithms in cyclic groups of order q ± 1.

On Intermediate Subalgebras of C*-simple Group Actions

2019 ◽  
Author(s):  
Tattwamasi Amrutam
Keyword(s):  
Simple Group ◽  
Large Class ◽  
Hyperbolic Group ◽  
Group Actions ◽  
Simple Groups ◽  
C Algebras ◽  
Amenable Radical

Abstract We show that for a large class of actions $\Gamma \curvearrowright \mathcal{A}$ of $C^*$-simple groups $\Gamma $ on unital $C^*$-algebras $\mathcal{A}$, including any non-faithful action of a hyperbolic group with trivial amenable radical, every intermediate $C^*$-subalgebra $\mathcal{B}$, $C_{\lambda }^*(\Gamma )\subseteq \mathcal{B} \subseteq \mathcal{A}\rtimes _{r}\Gamma $, is of the form $\mathcal{A}_1\rtimes _{r}\Gamma $, where $\mathcal{A}_1$ is a unital $\Gamma $-$C^*$-subalgebra of $\mathcal{A}$.

scholarly journals HOMOGENEITY OF THE PURE STATE SPACE FOR SEPARABLE C*-ALGEBRAS

2001 ◽  
Vol 12 (07) ◽  
pp. 813-845 ◽  
Author(s):  
HAJIME FUTAMURA ◽  
NOBUHIRO KATAOKA ◽  
AKITAKA KISHIMOTO
Keyword(s):  
Automorphism Group ◽  
State Space ◽  
Large Class ◽  
Pure State ◽  
C Algebras ◽  
Inner Automorphisms ◽  
Af Algebras

We prove that the pure state space is homogeneous under the action of the automorphism group (or a certain smaller group of approximately inner automorphisms) for a fairly large class of simple separable nuclear C*-algebras, including the approximately homogeneous C*-algebras and the class of purely infinite C*-algebras which has been recently classified by Kirchberg and Phillips. This extends the known results for UHF algebras and AF algebras by Powers and Bratteli.

scholarly journals Commuting elements in central products of special unitary groups

2012 ◽  
Vol 56 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Alejandro Adem ◽  
F. R. Cohen ◽  
José Manuel Gómez
Keyword(s):  
Prime Number ◽  
Moduli Space ◽  
Unitary Group ◽  
Unitary Groups ◽  
Connected Components ◽  
Flat Connections ◽  
Isomorphism Classes ◽  
Central Product ◽  
Central Products ◽  
Path Connected

AbstractWe study the space of commuting elements in the central product Gm,p of m copies of the special unitary group SU(p), where p is a prime number. In particular, a computation for the number of path-connected components of these spaces is given and the geometry of the moduli space Rep(ℤn, Gm,p) of isomorphism classes of flat connections on principal Gm,p-bundles over the n-torus is completely described for all values of n, m and p.

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