5,547 research outputs found
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
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
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
Three-dimensional theory of stimulated Raman scattering
We present a three-dimensional theory of stimulated Raman scattering
(SRS) or superradiance. In particular we address how the spatial and temporal
properties of the generated SRS beam, or Stokes beam, of radiation depends on
the spatial properties of the gain medium. Maxwell equations for the Stokes
field operators and of the atomic operators are solved analytically and a
correlation function for the Stokes field is derived. In the analysis we
identify a superradiating part of the Stokes radiation that exhibit beam
characteristics. We show how the intensity in this beam builds up in time and
at some point largely dominates the total Stokes radiation of the gain medium.
We show how the SRS depends on geometric factors such as the Fresnel number and
the optical depth, and that in fact these two factors are the only factors
describing the coherent radiation.Comment: 21 pages 14 figure
Estimates of Effective Hubbard Model Parameters for C20 isomers
We report on an effective Hubbard Hamiltonian approach for the study of
electronic correlations in C isomers, cage, bowl and ring, with quantum
Monte Carlo and exact diagonalization methods. The tight-binding hopping
parameter, , in the effective Hamiltonian is determined by a fit to density
functional theory calculations, and the on-site Coulomb interaction, , is
determined by calculating the isomers' affinity energies, which are compared to
experimental values. For the C fullerene cage we estimate eV and . The resulting
effective Hamiltonian is then used to study the shift of spectral peaks in the
density of states of neutral and one-electron-doped C isomers. Energy
gaps are also extracted for possible future comparison with experiments.Comment: 6 pages, 5 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
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