Operator Algebras
New submissions
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New submissions for Tue, 2 Dec 08
- [1] arXiv:0812.0077 [ps, pdf, other]
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Title: The Powers Sum of spatial CPD-semigroups and CP-semigroupsAuthors: Michael SkeideSubjects: Operator Algebras (math.OA)
We define spatial CPD-semigroup and construct their Powers sum. We construct the Powers sum for general spatial CP-semigroups. In both cases, we show that the product system of that Powers sum is the product of the spatial product systems of its factors. We show that on the domain of intersection, pointwise bounded CPD-semigroups on the one side and Schur CP-semigroups on the other, the constructions coincide. This summarizes all known results about Powers sums and generalizes them considerably.
- [2] arXiv:0812.0096 [ps, pdf, other]
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Title: C*-envelopes of tensor algebras for multivariable dynamicsComments: 21 pages, submitted to Proceedings of the Edinburgh Mathematical SocietySubjects: Operator Algebras (math.OA)
We give a new very concrete description of the C*-envelope of the tensor algebra associated to multivariable dynamical system. In the surjective case, this C*-envelope is described as a crossed product by an endomorphism, and as a groupoid C*-algebra. In the non-surjective case, it is a full corner of a such an algebra. We also show that when the space is compact, then the C*-envelope is simple if and only if the system is minimal.
- [3] arXiv:0812.0184 [ps, pdf, other]
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Title: Generalized Bunce-Deddens algebrasAuthors: Stefanos OrfanosSubjects: Operator Algebras (math.OA)
We define a broad class of crossed product C*-algebras of the form C(G)xG, where G is a discrete countable amenable residually finite group, and G is a profinite completion of G. We show that they are unital separable simple nuclear quasidiagonal C*-algebras, or real rank zero, stable rank one, with comparability of projections and with a unique trace.
- [4] arXiv:0812.0189 [ps, pdf, other]
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Title: Reduced free products of unital AH algebras and Blackadar and Kirchberg's MF algebrasComments: 29 pagesSubjects: Operator Algebras (math.OA)
In the paper, we prove that reduced free products of unital AH algebras with respect to given faithful tracial states, in the sense of Voiculescu, are Blackadar and Kirhcberg's MF algebras. We also show that the reduced free products of unital AH algebras with respect to given faithful tracial states, under mild conditions, are not quasidiagonal. Therefore we conclude, for a large class of AH algebras, the Brown-Douglas-Fillmore extension semigroups of the reduced free products of these AH algebras with respect to given faithful tracial states are not groups. Our result is based on Haagerup and Thorbj{\o}rsen's work on the reduced C$^*$-algebras of free groups.
- [5] arXiv:0812.0274 [ps, pdf, other]
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Title: Bose Einstein condensation on inhomogeneous amenable graphsComments: 42 pages, 10 figuresSubjects: Operator Algebras (math.OA); Mathematical Physics (math-ph)
We investigate the Bose-Einstein Condensation on nonhomogeneous amenable networks for the model describing arrays of Josephson junctions. The resulting topological model, whose Hamiltonian is the pure hopping one given by the opposite of the adjacency operator, has also a mathematical interest in itself. We show that for the nonhomogeneous networks like the comb graphs, particles condensate in momentum and configuration space as well. In this case different properties of the network, of geometric and probabilistic nature, such as the volume growth, the shape of the ground state, and the transience, all play a role in the condensation phenomena. The situation is quite different for homogeneous networks where just one of these parameters, e.g. the volume growth, is enough to determine the appearance of the condensation.
Cross-lists for Tue, 2 Dec 08
- [6] arXiv:0812.0037 (cross-list from math.GR) [ps, pdf, other]
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Title: New Presentations of Thompson's Groups and ApplicationsSubjects: Group Theory (math.GR); Operator Algebras (math.OA)
We find new presentations for the Thompson's groups $F$, the derived group $F^{'}$ and the intermediate group $D$. These presentations have a common ground in that their relators are the same and only the generating sets differ. As an application of these presentations we extract the following consequences: the cost of the group $F^{'}$ is 1 hence the cost cannot decide the (non)amenability question of $F$; the $II_1$ factor $L(F^{'})$ is inner asymptotically abelian and the reduced $C^*$-algebra of $F$ is not residually finite dimensional.
- [7] arXiv:0812.0089 (cross-list from math.PR) [ps, pdf, other]
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Title: Extending the Set of Quadratic Exponential VectorsSubjects: Probability (math.PR); Operator Algebras (math.OA)
We extend the square of white noise algebra over the step functions on R to the test function space of bounded square-integrable functions on R^d, and we show that in the Fock representation the exponential vectors exist for all test functions bounded by 1/2.
- [8] arXiv:0812.0154 (cross-list from math.AT) [ps, pdf, other]
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Title: Homotopy theory of C*-algebrasAuthors: Paul Arne ØstværSubjects: Algebraic Topology (math.AT); Operator Algebras (math.OA)
In this work we construct from ground up a homotopy theory of C*-algebras. This is achieved in parallel with the development of classical homotopy theory by first introducing an unstable model structure and second a stable model structure. The theory makes use of a full fledged import of homotopy theoretic techniques into the subject of C*-algebras.
The spaces in C*-homotopy theory are certain hybrids of functors represented by C*-algebras and spaces studied in classical homotopy theory. In particular, we employ both the topological circle and the C*-algebra circle of complex-valued continuous functions on the real numbers which vanish at infinity. By using the inner workings of the theory, we may stabilize the spaces by forming spectra and bispectra with respect to either one of these circles or their tensor product. These stabilized spaces or spectra are the objects of study in stable C*-homotopy theory.
The stable homotopy category of C*-algebras gives rise to invariants such as stable homotopy groups and bigraded cohomology and homology theories. We work out examples related to the emerging subject of noncommutative motives and zeta functions of C*-algebras. In addition, we employ homotopy theory to define a new type of K-theory of C*-algebras.
Replacements for Tue, 2 Dec 08
- [9] arXiv:0710.3423 (replaced) [ps, pdf, other]
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Title: Quasidiagonality of crossed productsAuthors: Stefanos OrfanosComments: Minor improvementsSubjects: Operator Algebras (math.OA)
- [10] arXiv:0810.0596 (replaced) [ps, pdf, other]
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Title: On quantum semigroup actions on finite quantum spacesAuthors: Piotr M. SoltanComments: A characterization of actions preserving a faithful state addedSubjects: Operator Algebras (math.OA); Quantum Algebra (math.QA)
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