107 research outputs found
Crossed Products by Dual Coactions of Groups and Homogeneous Spaces
Mansfield showed how to induce representations of crossed products of
C*-algebras by coactions from crossed products by quotient groups and proved an
imprimitivity theorem characterising these induced representations. We give an
alternative construction of his bimodule in the case of dual coactions, based
on the symmetric imprimitivity theorem of the third author; this provides a
more workable way of inducing representations of crossed products of
C*-algebras by dual coactions. The construction works for homogeneous spaces as
well as quotient groups, and we prove an imprimitivity theorem for these
induced representations.Comment: LaTeX-2e, 19 pages, requires pb-diagram.sty ((E) University of
Paderborn, Germany (K,R) University of Newcastle, Australia
Principal noncommutative torus bundles
In this paper we study continuous bundles of C*-algebras which are
non-commutative analogues of principal torus bundles. We show that all such
bundles, although in general being very far away from being locally trivial
bundles, are at least locally trivial with respect to a suitable bundle version
of bivariant K-theory (denoted RKK-theory) due to Kasparov. Using earlier
results of Echterhoff and Williams, we shall give a complete classification of
principal non-commutative torus bundles up to equivariant Morita equivalence.
We then study these bundles as topological fibrations (forgetting the group
action) and give necessary and sufficient conditions for any non-commutative
principal torus bundle being RKK-equivalent to a commutative one. As an
application of our methods we shall also give a K-theoretic characterization of
those principal torus-bundles with H-flux, as studied by Mathai and Rosenberg
which possess "classical" T-duals.Comment: 33 pages, to appear in the Proceedings of the London Mathematical
Societ
Naturality and Induced Representations
We show that induction of covariant representations for C*-dynamical systems
is natural in the sense that it gives a natural transformation between certain
crossed-product functors. This involves setting up suitable categories of
C*-algebras and dynamical systems, and extending the usual constructions of
crossed products to define the appropriate functors. From this point of view,
Green's Imprimitivity Theorem identifies the functors for which induction is a
natural equivalence. Various spcecial cases of these results have previously
been obtained on an ad hoc basis.Comment: LaTeX-2e, 24 pages, uses package pb-diagra
A Categorical Approach to Imprimitivity Theorems for C*-Dynamical Systems
Imprimitivity theorems provide a fundamental tool for studying the
representation theory and structure of crossed-product C*-algebras. In this
work, we show that the Imprimitivity Theorem for induced algebras, Green's
Imprimitivity Theorem for actions of groups, and Mansfield's Imprimitivity
Theorem for coactions of groups can all be viewed as natural equivalences
between various crossed-product functors among certain equivariant categories.
The categories involved have C*-algebras with actions or coactions (or both)
of a fixed locally compact group G as their objects, and equivariant
equivalence classes of right-Hilbert bimodules as their morphisms. Composition
is given by the balanced tensor product of bimodules.
The functors involved arise from taking crossed products; restricting,
inflating, and decomposing actions and coactions; inducing actions; and various
combinations of these.
Several applications of this categorical approach are also presented,
including some intriguing relationships between the Green and Mansfield
bimodules, and between restriction and induction of representations.Comment: LaTeX2e, 152 pages, uses class memo-l and packages amscd, xy, and
amssymb; fixed several typos and updated bibliograph
Non-Hausdorff Symmetries of C*-algebras
Symmetry groups or groupoids of C*-algebras associated to non-Hausdorff
spaces are often non-Hausdorff as well. We describe such symmetries using
crossed modules of groupoids. We define actions of crossed modules on
C*-algebras and crossed products for such actions, and justify these
definitions with some basic general results and examples.Comment: very minor changes. To appear in Math. An
Nonassociative strict deformation quantization of C*-algebras and nonassociative torus bundles
In this paper, we initiate the study of nonassociative strict deformation
quantization of C*-algebras with a torus action. We shall also present a
definition of nonassociative principal torus bundles, and give a classification
of these as nonassociative strict deformation quantization of ordinary
principal torus bundles. We then relate this to T-duality of principal torus
bundles with -flux. We also show that the Octonions fit nicely into our
theory.Comment: 15 pages, latex2e, exposition improved, to appear in LM
K-theory of noncommutative Bieberbach manifolds
We compute $K-theory of noncommutative Bieberbach manifolds, which quotients
of a three-dimensional noncommutative torus by a free action of a cyclic group
Z_N, N=2,3,4,6.Comment: 19 page
Die Evolution einer Standardarchitektur für Betriebliche Informationssysteme
Echterhoff D, Grasmugg S, Mersch S, Mönckemeyer M, Spitta T, Wrede S. Die Evolution einer Standardarchitektur für Betriebliche Informationssysteme. In: Spitta T, Borchers J, Sneed HM, eds. Software-Management 2002. LNI. Vol P-23. Bonn: GI e.V.; 2002: 131-142.The paper outlines the history of a standard architecture for small and medium sized administrative systems. It has been developped 1985 in the Schering AG / Berlin, and applied in several firms over more than 15 years. Some of the about 150 applications, developped and maintained by more than 100 programmers, are still in operation. In 1999 a revision of the architecture and a new implementation in Java was started. The latest version is a four-level-architecture for distributed systems with a browser as user interface. Aside architectural considerations we discuss some of our design and implementation experiences with java
Equivariant comparison of quantum homogeneous spaces
We prove the deformation invariance of the quantum homogeneous spaces of the
q-deformation of simply connected simple compact Lie groups over the
Poisson-Lie quantum subgroups, in the equivariant KK-theory with respect to the
translation action by maximal tori. This extends a result of Neshveyev-Tuset to
the equivariant setting. As applications, we prove the ring isomorphism of the
K-group of Gq with respect to the coproduct of C(Gq), and an analogue of the
Borsuk-Ulam theorem for quantum spheres.Comment: 21 page
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