111 research outputs found
Quantum differential forms
Formalism of differential forms is developed for a variety of Quantum and
noncommutative situations
On the lifting of the Nagata automorphism
It is proved that the Nagata automorphism (Nagata coordinates, respectively)
of the polynomial algebra over a field cannot be lifted to a
-automorphism (-coordinate, respectively) of the free associative algebra
. The proof is based on the following two new results which have
their own interests: degree estimate of and tameness of
the automorphism group .Comment: 15 page
Degenerations of ideal hyperbolic triangulations
Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The
deformation variety D(T), a subset of which parameterises (incomplete)
hyperbolic structures obtained on M using T, is defined and compactified by
adding certain projective classes of transversely measured singular
codimension-one foliations of M. This leads to a combinatorial and geometric
variant of well-known constructions by Culler, Morgan and Shalen concerning the
character variety of a 3-manifold.Comment: 31 pages, 11 figures; minor changes; to appear in Mathematische
Zeitschrif
Experimental study of weak antilocalization effect in a high mobility InGaAs/InP quantum well
The magnetoresistance associated with quantum interference corrections in a
high mobility, gated InGaAs/InP quantum well structure is studied as a function
of temperature, gate voltage, and angle of the tilted magnetic field.
Particular attention is paid to the experimental extraction of phase-breaking
and spin-orbit scattering times when weak anti- localization effects are
prominent. Compared with metals and low mobility semiconductors the
characteristic magnetic field in high mobility
samples is very small and the experimental dependencies of the interference
effects extend to fields several hundreds of times larger. Fitting experimental
results under these conditions therefore requires theories valid for arbitrary
magnetic field. It was found, however, that such a theory was unable to fit the
experimental data without introducing an extra, empirical, scale factor of
about 2. Measurements in tilted magnetic fields and as a function of
temperature established that both the weak localization and the weak
anti-localization effects have the same, orbital origin. Fits to the data
confirmed that the width of the low field feature, whether a weak localization
or a weak anti-localization peak, is determined by the phase-breaking time and
also established that the universal (negative) magnetoresistance observed in
the high field limit is associated with a temperature independent spin-orbit
scattering time.Comment: 13 pages including 10 figure
Representation theory of super Yang-Mills algebras
We study in this article the representation theory of a family of super
algebras, called the \emph{super Yang-Mills algebras}, by exploiting the
Kirillov orbit method \textit{\`a la Dixmier} for nilpotent super Lie algebras.
These super algebras are a generalization of the so-called \emph{Yang-Mills
algebras}, introduced by A. Connes and M. Dubois-Violette in \cite{CD02}, but
in fact they appear as a "background independent" formulation of supersymmetric
gauge theory considered in physics, in a similar way as Yang-Mills algebras do
the same for the usual gauge theory. Our main result states that, under certain
hypotheses, all Clifford-Weyl super algebras \Cliff_{q}(k) \otimes A_{p}(k),
for , or and , appear as a quotient of all super
Yang-Mills algebras, for and . This provides thus a family
of representations of the super Yang-Mills algebras
Does theory of quantum correction to conductivity agree with experimental data in 2D systems?
The quantum correction to the conductivity have been studied in two types of
2D heterostructures: with doped quantum well and doped barriers. The consistent
analysis shows that in the structures where electrons occupy the states in
quantum well only, all the temperature and magnetic field dependencies of the
components of resistivity tensor are well described by the theories of quantum
corrections. The contribution of electron-electron interaction to the
conductivity have been determined reliably in the structures with different
electron density. A possible reason of large scatter in experimental data
concerning the contribution of electron-electron interaction, obtained in
previous papers, and the role of the carriers, occupied the states of the doped
layers, is discussed.Comment: 10 pages with 9 figure
Constructions of free commutative integro-differential algebras
In this survey, we outline two recent constructions of free commutative
integro-differential algebras. They are based on the construction of free
commutative Rota-Baxter algebras by mixable shuffles. The first is by
evaluations. The second is by the method of Gr\"obner-Shirshov bases.Comment: arXiv admin note: substantial text overlap with arXiv:1302.004
A Review of Magnetic Phenomena in Probe-Brane Holographic Matter
Gauge/gravity duality is a useful and efficient tool for addressing and
studying questions related to strongly interacting systems described by a gauge
theory. In this manuscript we will review a number of interesting phenomena
that occur in such systems when a background magnetic field is turned on.
Specifically, we will discuss holographic models for systems that include
matter fields in the fundamental representation of the gauge group, which are
incorporated by adding probe branes into the gravitational background dual to
the gauge theory. We include three models in this review: the D3-D7 and D4-D8
models, that describe four-dimensional systems, and the D3-D7' model, that
describes three-dimensional fermions interacting with a four-dimensional gauge
field.Comment: 35 pages, 27 figures, to appear in Lect. Notes Phys. "Strongly
interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K.
Landsteiner, A. Schmitt, H.-U. Yee; references adde
Nonstable K-Theory for graph algebras
We compute the monoid V (LK(E)) of isomorphism classes of finitely generated
projective modules over certain graph algebras LK(E), and we show that this monoid satisfies
the refinement property and separative cancellation. We also show that there is a natural
isomorphism between the lattice of graded ideals of LK(E) and the lattice of order-ideals
of V (LK(E)). When K is the field C of complex numbers, the algebra LC(E) is a dense
subalgebra of the graph C -algebra C (E), and we show that the inclusion map induces an
isomorphism between the corresponding monoids. As a consequence, the graph C*-algebra
of any row-finite graph turns out to satisfy the stable weak cancellation propert
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This work was supported by National Institute of Biomedical Imaging and Bioengineering Grant No. U54EB020403 (to the ENIGMA consortium)
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