139 research outputs found
The K-theory of free quantum groups
In this paper we study the K -theory of free quantum groups in the sense of Wang and Van Daele, more precisely, of free products of free unitary and free orthogonal quantum groups. We show that these quantum groups are K -amenable and establish an analogue of the PimsnerâVoiculescu exact sequence. As a consequence, we obtain in particular an explicit computation of the K -theory of free quantum groups. Our approach relies on a generalization of methods from the BaumâConnes conjecture to the framework of discrete quantum groups. This is based on the categorical reformulation of the BaumâConnes conjecture developed by Meyer and Nest. As a main result we show that free quantum groups have a Îł -element and that Îł=1 . As an important ingredient in the proof we adapt the Dirac-dual Dirac method for groups acting on trees to the quantum case. We use this to extend some permanence properties of the BaumâConnes conjecture to our setting
Twisting and Rieffel's deformation of locally compact quantum groups. Deformation of the Haar measure
We develop the twisting construction for locally compact quantum groups. A
new feature, in contrast to the previous work of M. Enock and the second
author, is a non-trivial deformation of the Haar measure. Then we construct
Rieffel's deformation of locally compact quantum groups and show that it is
dual to the twisting. This allows to give new interesting concrete examples of
locally compact quantum groups, in particular, deformations of the classical
group and of the Woronowicz' quantum group
Quantum Isometries of the finite noncommutative geometry of the Standard Model
We compute the quantum isometry group of the finite noncommutative geometry F
describing the internal degrees of freedom in the Standard Model of particle
physics. We show that this provides genuine quantum symmetries of the spectral
triple corresponding to M x F where M is a compact spin manifold. We also prove
that the bosonic and fermionic part of the spectral action are preserved by
these symmetries.Comment: 29 pages, no figures v3: minor change
Sequential design of computer experiments for the estimation of a probability of failure
This paper deals with the problem of estimating the volume of the excursion
set of a function above a given threshold,
under a probability measure on that is assumed to be known. In
the industrial world, this corresponds to the problem of estimating a
probability of failure of a system. When only an expensive-to-simulate model of
the system is available, the budget for simulations is usually severely limited
and therefore classical Monte Carlo methods ought to be avoided. One of the
main contributions of this article is to derive SUR (stepwise uncertainty
reduction) strategies from a Bayesian-theoretic formulation of the problem of
estimating a probability of failure. These sequential strategies use a Gaussian
process model of and aim at performing evaluations of as efficiently as
possible to infer the value of the probability of failure. We compare these
strategies to other strategies also based on a Gaussian process model for
estimating a probability of failure.Comment: This is an author-generated postprint version. The published version
is available at http://www.springerlink.co
Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices
A reducible representation of the Temperley-Lieb algebra is constructed on
the tensor product of n-dimensional spaces. One obtains as a centraliser of
this action a quantum algebra (a quasi-triangular Hopf algebra) U_q with a
representation ring equivalent to the representation ring of the sl_2 Lie
algebra. This algebra U_q is the symmetry algebra of the corresponding open
spin chain.Comment: 14 pages LaTex; typos corrected and two references adde
A maximality result for orthogonal quantum groups
We prove that the quantum group inclusion is "maximal",
where is the usual orthogonal group and is the half-liberated
orthogonal quantum group, in the sense that there is no intermediate compact
quantum group . In order to prove this result, we
use: (1) the isomorphism of projective versions , (2) some
maximality results for classical groups, obtained by using Lie algebras and
some matrix tricks, and (3) a short five lemma for cosemisimple Hopf algebras.Comment: 10 page
Production of and mesons in UU collisions at GeV
The PHENIX experiment at the Relativistic Heavy Ion Collider measured
and mesons at midrapidity in UU collisions at
GeV in a wide transverse momentum range. Measurements were performed in the
decay modes. A strong suppression of
and meson production at high transverse momentum was observed in
central UU collisions relative to binary scaled results. Yields of
and mesons measured in UU collisions show similar suppression
pattern to the ones measured in AuAu collisions at
GeV for similar numbers of participant nucleons. The / ratios do
not show dependence on centrality or transverse momentum, and are consistent
with previously measured values in hadron-hadron, hadron-nucleus,
nucleus-nucleus, and collisions.Comment: 403 authors from 72 institutions, 13 pages, 6 figures, 7 tables, 2012
data. v2 is version accepted by Physical Review C. Plain text data tables for
the points plotted in figures for this and previous PHENIX publications are
(or will be) publicly available at http://www.phenix.bnl.gov/papers.htm
Measurement of jet-medium interactions via direct photon-hadron correlations in AuAu and Au collisions at GeV
We present direct photon-hadron correlations in 200 GeV/A AuAu, Au
and collisions, for direct photon from 5--12 GeV/, collected
by the PHENIX Collaboration in the years from 2006 to 2011. We observe no
significant modification of jet fragmentation in Au collisions,
indicating that cold nuclear matter effects are small or absent. Hadrons
carrying a large fraction of the quark's momentum are suppressed in AuAu
compared to and Au. As the momentum fraction decreases, the
yield of hadrons in AuAu increases to an excess over the yield in
collisions. The excess is at large angles and at low hadron and is most
pronounced for hadrons associated with lower momentum direct photons.
Comparison to theoretical calculations suggests that the hadron excess arises
from medium response to energy deposited by jets.Comment: 578 authors from 80 institutions, 11 pages, 7 figures, data from
2007, 2008, 2010, and 2011. v2 is version accepted for publication in
Physical Review C. Plain text data tables for the points plotted in figures
for this and previous PHENIX publications are (or will be) publicly available
at http://www.phenix.bnl.gov/papers.htm
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