598 research outputs found
Leavitt -algebras over countable graphs embed into
For a commutative ring with unit we show that the Leavitt path algebra
of a graph embeds into precisely when is countable.
Before proving this result we prove a generalised Cuntz-Krieger Uniqueness
Theorem for Leavitt path algebras over .Comment: 17 pages. At the request of a referee the previous version of this
paper has been split into two papers. This version is the first of these
papers. The second will also be uploaded to the arXi
does not embed in
For a commutative ring with unit we investigate the embedding of tensor
product algebras into the Leavitt algebra . We show that the tensor
product does not embed in
(as a unital -algebra). We also prove a partial
non-embedding result for the more general . Our
techniques rely on realising Thompson's group as a subgroup of the unitary
group of .Comment: 16 pages. At the request of a referee the paper arXiv:1503.08705v2
was split into two papers. This is the second of those paper
The Cuntz splice does not preserve -isomorphism of Leavitt path algebras over
We show that the Leavitt path algebras and
are not isomorphic as -algebras. There are two key
ingredients in the proof. One is a partial algebraic translation of Matsumoto
and Matui's result on diagonal preserving isomorphisms of Cuntz--Krieger
algebras. The other is a complete description of the projections in
for a finite graph. This description is based on a
generalization, due to Chris Smith, of the description of the unitaries in
given by Brownlowe and the second named author. The
techniques generalize to a slightly larger class of rings than just
.Comment: 17 pages. Since version 2 we extended the arguments from Z to more
general ring
Almost Commuting Orthogonal Matrices
We show that almost commuting real orthogonal matrices are uniformly close to
exactly commuting real orthogonal matrices. We prove the same for symplectic
unitary matrices. This is in contrast to the general complex case, where not
all pairs of almost commuting unitaries are close to commuting pairs. Our
techniques also yield results about almost normal matrices over the reals and
the quaternions.Comment: 13 pages, 3 figure
Invariance of the Cuntz splice
We show that the Cuntz splice induces stably isomorphic graph -algebras.Comment: Our arguments to prove invariance of the Cuntz splice for unital
graph C*-algebras in arXiv:1505.06773 applied with only minor changes in the
general case. Since most of the results of that preprint have since been
superseded by other forthcoming work, we do not intend to publish it, whereas
this work is intended for publication. arXiv admin note: substantial text
overlap with arXiv:1505.0677
Amplified graph C*-algebras
We provide a complete invariant for graph C*-algebras which are amplified in
the sense that whenever there is an edge between two vertices, there are
infinitely many. The invariant used is the standard primitive ideal space
adorned with a map into {-1,0,1,2,...}, and we prove that the classification
result is strong in the sense that isomorphisms at the level of the invariant
always lift. We extend the classification result to cover more graphs, and give
a range result for the invariant (in the vein of Effros-Handelman-Shen) which
is further used to prove that extensions of graph C*-algebras associated to
amplified graphs are again graph C*-algebras of amplified graphs.Comment: 15 pages, 1 figur
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