2,352 research outputs found
Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs
In previous work, the authors showed that the C*-algebra C*(\Lambda) of a
row-finite higher-rank graph \Lambda with no sources is simple if and only if
\Lambda is both cofinal and aperiodic. In this paper, we generalise this result
to row-finite higher-rank graphs which are locally convex (but may contain
sources). Our main tool is Farthing's "removing sources" construction which
embeds a row-finite locally convex higher-rank graph in a row-finite
higher-rank graph with no sources in such a way that the associated C*-algebras
are Morita equivalent.Comment: 18 pages, 1 figure, figure drawn using Tikz/PGF. Version 2: the
hypothesis "with no sources" has been removed from Theorem 3.4; it appeared
there in error since the main point of the theorem is that it applies in the
absence of this hypothesis (cf Theorem 3.1 of arXiv:math/0602120
Unbounded quasitraces, stable finiteness and pure infiniteness
We prove that if A is a \sigma-unital exact C*-algebra of real rank zero,
then every state on K_0(A) is induced by a 2-quasitrace on A. This yields a
generalisation of Rainone's work on pure infiniteness and stable finiteness of
crossed products to the non-unital case. It also applies to k-graph algebras
associated to row-finite k-graphs with no sources. We show that for any k-graph
whose C*-algebra is unital and simple, either every twisted C*-algebra
associated to that k-graph is stably finite, or every twisted C*-algebra
associated to that k-graph is purely infinite. Finally we provide sufficient
and necessary conditions for a unital simple k-graph algebra to be purely
infinite in terms of the underlying k-graph.Comment: 38 page
Allocating and splitting free energy to maximize molecular machine flux
Biomolecular machines transduce between different forms of energy. These
machines make directed progress and increase their speed by consuming free
energy, typically in the form of nonequilibrium chemical concentrations.
Machine dynamics are often modeled by transitions between a set of discrete
metastable conformational states. In general, the free energy change associated
with each transition can increase the forward rate constant, decrease the
reverse rate constant, or both. In contrast to previous optimizations, we find
that in general flux is neither maximized by devoting all free energy changes
to increasing forward rate constants nor by solely decreasing reverse rate
constants. Instead the optimal free energy splitting depends on the detailed
dynamics. Extending our analysis to machines with vulnerable states (from which
they can break down), in the strong driving corresponding to in vivo cellular
conditions, processivity is maximized by reducing the occupation of the
vulnerable state.Comment: 22 pages, 7 figure
The Noncommutative Geometry of k-graph C*-Algebras
This paper is comprised of two related parts. First we discuss which k-graph
algebras have faithful gauge invariant traces, where the gauge action of \T^k
is the canonical one. We give a sufficient condition for the existence of such
a trace, identify the C*-algebras of k-graphs satisfying this condition up to
Morita equivalence, and compute their K-theory.
For k-graphs with faithful gauge invariant trace, we construct a smooth
-summable semifinite spectral triple. We use the semifinite local
index theorem to compute the pairing with K-theory. This numerical pairing can
be obtained by applying the trace to a KK-pairing with values in the K-theory
of the fixed point algebra of the \T^k action. As with graph algebras, the
index pairing is an invariant for a finer structure than the isomorphism class
of the algebra.Comment: 38 pages, some pictures drawn in picTeX Some minor technical
revisions. Material has been reorganised with detailed discussion of k-graphs
admitting graph traces shortened and moved to an appendix. This version to
appear in K-theor
C*-algebras associated to coverings of k-graphs
A covering of k-graphs (in the sense of Pask-Quigg-Raeburn) induces an
embedding of universal C*-algebras. We show how to build a (k+1)-graph whose
universal algebra encodes this embedding. More generally we show how to realise
a direct limit of k-graph algebras under embeddings induced from coverings as
the universal algebra of a (k+1)-graph. Our main focus is on computing the
K-theory of the (k+1)-graph algebra from that of the component k-graph
algebras.
Examples of our construction include a realisation of the Kirchberg algebra
\mathcal{P}_n whose K-theory is opposite to that of \mathcal{O}_n, and a class
of AT-algebras that can naturally be regarded as higher-rank Bunce-Deddens
algebras.Comment: 44 pages, 2 figures, some diagrams drawn using picTeX. v2. A number
of typos corrected, some references updated. The statements of Theorem 6.7(2)
and Corollary 6.8 slightly reworded for clarity. v3. Some references updated;
in particular, theorem numbering of references to Evans updated to match
published versio
KMS states on generalised Bunce-Deddens algebras and their Toeplitz extensions
We study the generalised Bunce-Deddens algebras and their Toeplitz extensions
constructed by Kribs and Solel from a directed graph and a sequence of
positive integers. We describe both of these -algebras in terms of novel
universal properties, and prove uniqueness theorems for them; if
determines an infinite supernatural number, then no aperiodicity hypothesis is
needed in our uniqueness theorem for the generalised Bunce-Deddens algebra. We
calculate the KMS states for the gauge action in the Toeplitz algebra when the
underlying graph is finite. We deduce that the generalised Bunce-Deddens
algebra is simple if and only if it supports exactly one KMS state, and this is
equivalent to the terms in the sequence all being coprime with the
period of the underlying graph.Comment: 30 pages. This version includes a section on the topological graph
, which allows us to use the work of Katsura to obtain a
uniqueness theorem for , and a characterisation of the ideal
structure of when is finite and strongly connected. The
introduction and references have been updated. Minor typos have been
correcte
Groupoid algebras as Cuntz-Pimsner algebras
We show that if is a second countable locally compact Hausdorff \'etale
groupoid carrying a suitable cocycle , then the reduced
-algebra of can be realised naturally as the Cuntz-Pimsner algebra of
a correspondence over the reduced -algebra of the kernel of . If
the full and reduced -algebras of coincide, we deduce that the full
and reduced -algebras of coincide. We obtain a six-term exact sequence
describing the -theory of in terms of that of .Comment: 5 pages. V2: James Fletcher discovered an error Lemma 9. No other
results are affected. In this version, statements (2) and (3), and the proof,
of Lemma 9 have been corrected. Remark 10 has been added to give details of
the error. An erratum will appear in Math Scand, referring to this version of
the arXiv posting for detail
A dual graph construction for higher-rank graphs, and -theory for finite 2-graphs
Given a -graph and an element of \NN^k, we define the dual
-graph, . We show that when is row-finite and has no
sources, the -algebras and coincide. We use
this isomorphism to apply Robertson and Steger's results to calculate the
-theory of when is finite and strongly connected
and satisfies the aperiodicity condition.Comment: 9 page
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