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Showing 1 to 20 of 40 for “"C*-algebra"”.
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Cohomological dimension for C*-algebras
We define and explore invariants for C*-algebras that arise as cohomological dimensions for associated categories of operator space modules. The setting of exact categories provides us with a robust framework to utilise homological techniques.<br/><br/>We develop initial global dimension theorems …
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partial translation algebras for certain discrete metric spaces
The notion of a partial translation algebra was introduced by Brodzki, Niblo<br/>and Wright in [11] to provide an analogue of the reduced group C*-algebra<br/>for metric spaces. Such an algebra is constructed from a partial translation<br/>structure, a structure which any bounded geometry uniformly …
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Quasi-Pure E0-Semigroups
… quasi-pure E0-semigroups acting on a von Neumann algebra as that with equal tail and fixed-point algebras and we describe these notable algebras for E0-semigroups of B(H) where H is a separable Hilbert space. We consider the classes of pure, quasi-pure and ergodic E0-semigroups induced by …
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MF algebras and a Bishop -Stone -Weierstrass theorem result
… first part, we obtain many new results about MF algebras. First, we continue the work on D. Voiculescu's topological free entropy dimension deltatop (x1, ..., xn) for an n-tuple x&ar; = (x1, ..., xn) of elements in a unital C*-algebra. We also introduce a new invariant that is a C*-algebra analog …
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C*-algebras of the planar crystal groups and their irreducible *-representations
… is the explicit construction of the group C*-Algebra C*(G) for each of the seventeen planar crystal groups G. A secondary result is the explicit description of all the irreducible *-representations of these C*-Algebras. Two further applications are described in the concluding paragraph below. …
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Representation of non-commutative topological algebras
… enables us to represent a complex commutative C*-algebra as a full algebra of complex valued functions defined on its set of primitive ideals which is called the structure space of the algebra. In is thesis we are concerned with the generalization of this type of representation theorem to …
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On approximation properties of group C* - algebras
… of an approximation property for the reduced C*- algebra of a group: the invariant approximation property. This statement captures a particular relationship between three important operator algebras associated with a group: the reduced C*- algebra, the von Neumann algebra, and the uniform Roe …
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Dynamical C*-Algebras and Quadratic Perturbations for Fermions
… spacetimes in the context of dynamical C*-algebras. Our focus is on a particular class of interactions, that of kinetic perturbations; we provide their definition and we show that these induce, in the fermionic dynamical C*-algebra, symbols that obey the canonical anticommutation relation …
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Quantum Metrics on Approximately Finite-Dimensional Algebras
… bringing approximately finite-dimensional (AF) algebras into the realm of noncommutative metric geometry. We construct quantum metric structures on unital AF algebras equipped with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive …
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Nonunital multiplier pairs and remarks on generalized group C*-algebras
… T and let B (f, g) denote the universal C*-algebra generated by U and V subject to the conditions that U and V are a unitary, and Uf( V)U-1 = g( V). We then will prove that this C*-algebra may be represented as a crossed product. Next we will show that under certain conditions on f or g, B …
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Multipliers of dynamical systems
… very useful in the study of the reduced C∗-algebra of a locally compact group. There is also a rich connection to Schur multipliers,which have been studied since the early twentieth century, and have a large number of applications.<br/><br/>We develop a theory of Herz–Schur multipliers of a …
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Operator Algebras and Abstract Classification
… to the study of operator spaces, operator algebras, and their automorphisms using methods from logic, particularly descriptive set theory and model theory. The material is divided into three main themes. The first one concerns the notion of Polish groupoids and functorial complexity. Such a …
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Generalized Fixed-Point Algebras for Twisted C*-Dynamical Systems
In his paper “Generalized Fixed Point Algebras and Square-Integrable Group Actions,” Ralf Meyer showed how to construct generalized fixed-point algebras for C*-dynamical systems via their square-integrable representations on Hilbert C*-modules. His method extends Marc Rieffel’s construction of …
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Relating Thompson's group V to graphs of groups and Hecke algebras
… Pask, Spielberg and Thomas constructed a $C^*$-algebra for a graph of groups, writtten $C^*(\mathcal{G})$, which bears many similarities to the $C^*$-algebra of a directed graph $G$. Inspired by the fact that directed graph $C^*$-algebras $C^*(G)$ have algebraic analogues in Leavitt path …
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Partial dynamical systems and AF C*-algebras
<p>By utilizing the connections between C*-algebras, groupoids, and inverse semigroups, we obtain a characterization theorem, in terms of dynamical systems, of approximately finite-dimensional (AF) C*-algebras. The dynamical systems considered in this characterization consist of partially defined …
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OPERATOR RANGES OF SHIFTS AND C*-ALGEBRAS (STRANGE RANGE, QUASI-SIMILARITY, LATTICE)
… the ranges of operators from a commutative C*-algebra form a lattice under intersection and vector sum. If P and Q are projections in B(H) with non zero intersection and so that the angle between their ranges is 0, then it is shown that the ranges of the operators in the C*-algebra generated by …
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A p-adic spectral triple
<p>We construct a spectral triple for the C*-algebra of continuous functions on the space of <em>p</em>-adic integers. On the technical level we utilize a weighted rooted tree obtained from a coarse grained approximation of the space combined with the forward derivative <em>D</em> on the tree. Our …
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Non-abelian duality for C*- algebraic covariant structures
… {(d, "), (a, n), (a, d)} formadas por una C*-algebra "cy' separable, una acción torcida medible (a, a) de un gnrpo localmente compacto segundo-contable G, otra acción torcida medible (á, d) de otro grupo localmente compacto segundo-contable G y una función estrictamente continua ,s : G x G -+ …
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Properties of Pure Completely Positive Linear Maps of Operator Systems
… operator system spanned in the group C*-algebra C*(Fn) by the n generators of the free group Fn and their inverses, then the identity map in : Sn -> Sn is shown to be a pure completely positive map. Similarly, the identity map jn : NC(n) -> NC(n) on the noncommutative n-cube NC(n) in the …
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