224 research outputs found
Ideal structure of -algebras associated with -correspondences
We study the ideal structure of -algebras arising from
-correspondences. We prove that gauge-invariant ideals of our
-algebras are parameterized by certain pairs of ideals of original
-algebras. We show that our -algebras have a nice property which
should be possessed by generalization of crossed products. Applications to
crossed products by Hilbert -bimodules and relative Cuntz-Pimsner algebras
are also discussed.Comment: 34 page
A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras I, fundamental results
We introduce a new class of C^*-algebras, which is a generalization of both
graph algebras and homeomorphism C^*-algebras. This class is very large and
also very tractable. We prove the so-called gauge-invariant uniqueness theorem
and the Cuntz-Krieger uniqueness theorem, and compute the K-groups of our
algebras.Comment: 37 pages, some terminologies changed, for example,
C^*-correspondences were called Hilbert C^*-bimodules and topological graphs
were called continuous graph
The ideal structures of crossed products of Cuntz algebras by quasi-free actions of abelian groups
We completely determine the ideal structures of the crossed products of Cuntz
algebras by quasi-free actions of abelian groups and give another proof of A.
Kishimoto's result on the simplicity of such crossed products. We also give a
necessary and sufficient condition that our algebras become primitive, and
compute the Connes spectra and K-groups of our algebras
C^*-algebras generated by scaling elements
We investigate C^*-algebras generated by scaling elements. We generalize the
Wold decomposition and Coburn's theorem on isometries to scaling elements. We
also completely determine when the C^*-algebra generated by a scaling element
contains an infinite projection.Comment: 8 page
A class of -algebras generalizing both graph algebras and homeomorphism -algebras IV, pure infiniteness
This is the final one in the series of papers where we introduce and study
the -algebras associated with topological graphs. In this paper, we get a
sufficient condition on topological graphs so that the associated
-algebras are simple and purely infinite. Using this result, we give one
method to construct all Kirchberg algebras as -algebras associated with
topological graphs.Comment: 28 page
A construction of actions on Kirchberg algebras which induce given actions on their K-groups
We prove that every action of a finite group all of whose Sylow subgroups are
cyclic on the K-theory of a Kirchberg algebra can be lifted to an action on the
Kirchberg algebra. The proof uses a construction of Kirchberg algebras
generalizing the one of Cuntz-Krieger algebras, and a result on modules over
finite groups. As a corollary, every automorphism of the K-theory of a
Kirchberg algebra can be lifted to an automorphism of the Kirchberg algebra
with same order.Comment: 34 pages, Corrected typo
A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras III, ideal structures
We investigate the ideal structures of the C^*-algebras arising from
topological graphs. We give the complete description of ideals of such
C^*-algebras which are invariant under the so-called gauge action, and give the
condition on topological graphs so that all ideals are invariant under the
gauge action. We get conditions for our C^*-algebras to be simple, prime or
primitive. We completely determine the prime ideals, and show that most of them
are primitive. Finally, we construct a discrete graph such that the associated
C^*-algebra is prime but not primitive.Comment: 47 pages, typos corrected, Sections 11 and 12 Change
A construction of -algebras from -correspondences
We introduce a method to define -algebras from -correspondences.
Our construction generalizes Cuntz-Pimsner algebras, crossed products by
Hilbert -modules, and graph algebras.Comment: 10 pages, to appear in Contemp. Math., Proceedings of the AMS
conference "Advances in Quantum Dynamics
A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras II, examples
We show that the method to construct C^*-algebras from topological graphs,
introduced in our previous paper, generalizes many known constructions. We give
many ways to make new topological graphs from old ones, and study the relation
of C^*-algebras constructed from them. We also prove that our C^*-algebras have
a certain characterization. This gives us another definition of our
C^*-algebras.Comment: 38 page
Permutation presentations of modules over finite groups
We introduce a notion of permutation presentations of modules over finite
groups, and completely determine finite groups over which every module has a
permutation presentation. To get this result, we prove that every coflasque
module over a cyclic p-group is permutation projective.Comment: 12 page
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