24 research outputs found
Integration over the quantum diagonal subgroup and associated Fourier-like algebras
By analogy with the classical construction due to Forrest, Samei and Spronk
we associate to every compact quantum group a completely
contractive Banach algebra , which can be viewed as a
deformed Fourier algebra of . To motivate the construction we first
analyse in detail the quantum version of the integration over the diagonal
subgroup, showing that although the quantum diagonal subgroups in fact never
exist, as noted earlier by Kasprzak and So{\l}tan, the corresponding
integration represented by a certain idempotent state on makes
sense as long as is of Kac type. Finally we analyse as an explicit
example the algebras , , associated to Wang's free
orthogonal groups, and show that they are not operator weakly amenable.Comment: Minor updates; Remark 5.7 has been added; 31 page
A Characterization of right coideals of quotient type and its application to classification of Poisson boundaries
Let be a co-amenable compact quantum group. We show that a right coideal
of is of quotient type if and only if it is the range of a conditional
expectation preserving the Haar state and is globally invariant under the left
action of the dual discrete quantum group. We apply this result to theory of
Poisson boundaries introduced by Izumi for discrete quantum groups and
generalize a work of Izumi-Neshveyev-Tuset on for co-amenable compact
quantum groups with the commutative fusion rules. More precisely, we prove that
the Poisson integral is an isomorphism between the Poisson boundary and the
right coideal of quotient type by maximal quantum subgroup of Kac type. In
particular, the Poisson boundary and the quantum flag manifold are isomorphic
for any q-deformed classical compact Lie group.Comment: 28 pages, Remark 4.9 adde
The nature of the unresolved extragalactic soft CXB
In this paper we investigate the power spectrum of the unresolved 0.5-2 keV
CXB with deep Chandra 4 Ms observations in the CDFS. We measured a signal
which, on scales >30", is significantly higher than the Shot-Noise and is
increasing with the angular scale. We interpreted this signal as the joint
contribution of clustered undetected sources like AGN, Galaxies and
Inter-Galactic-Medium (IGM). The power of unresolved cosmic sources
fluctuations accounts for \sim 12% of the 0.5-2 keV extragalactic CXB. Overall,
our modeling predicts that \sim 20% of the unresolved CXB flux is made by low
luminosity AGN, \sim 25% by galaxies and \sim 55% by the IGM (Inter Galactic
Medium). We do not find any direct evidence of the so called Warm Hot
Intergalactic Medium (i.e. matter with 10^5K<T<10^7K and density contrast
{\delta} <1000), but we estimated that it could produce about 1/7 of the
unresolved CXB. We placed an upper limit to the space density of postulated
X-ray-emitting early black hole at z>7.5 and compared it with SMBH evolution
models.Comment: 15 pages, 9 figures, accepted by MNRA
On the cosmic evolution of the scaling relations between black holes and their host galaxies: Broad Line AGN in the zCOSMOS survey
(Abriged) We report on the measurement of the rest frame K-band luminosity
and total stellar mass of the hosts of 89 broad line Active Galactic Nuclei
detected in the zCOSMOS survey in the redshift range 1<z<2.2. The unprecedented
multiwavelength coverage of the survey field allows us to disentangle the
emission of the host galaxy from that of the nuclear black hole in their
Spectral Energy Distributions. We derive an estimate of black hole masses
through the analysis of the broad Mg II emission lines observed in the
medium-resolution spectra taken with VIMOS/VLT as part of the zCOSMOS project.
We found that, as compared to the local value, the average black hole to host
galaxy mass ratio appears to evolve positively with redshift, with a best fit
evolution of the form (1+z)^{0.68 \pm0.12 +0.6 -0.3}, where the large
asymmetric systematic errors stem from the uncertainties in the choice of IMF,
in the calibration of the virial relation used to estimate BH masses and in the
mean QSO SED adopted. A thorough analysis of observational biases induced by
intrinsic scatter in the scaling relations reinforces the conclusion that an
evolution of the MBH-M* relation must ensue for actively growing black holes at
early times: either its overall normalization, or its intrinsic scatter (or
both) appear to increase with redshift. This can be interpreted as signature of
either a more rapid growth of supermassive black holes at high redshift, a
change of structural properties of AGN hosts at earlier times, or a significant
mismatch between the typical growth times of nuclear black holes and host
galaxies.Comment: 47 pages, 8 figures. Accepted for publication in Ap
A new measurement of the cosmic X-ray background
We present a new measurement of the cosmic X-ray background (CXRB) in the
1.5-7 keV energy band, performed by exploiting the Swift X-ray telescope (XRT)
data archive. We also present a CXRB spectral model in a wider energy band
(1.5-200 keV), obtained by combining these data with the recently published
Swift-BAT measurement. From the XRT archive we collect a complete sample of 126
high Galactic latitude gamma-ray burst (GRB) follow-up observations. This
provides a total exposure of 7.5 Ms and a sky-coverage of 7 square degrees
which represents a serendipitous survey, well suited for a direct measurement
of the CXRB in the 1.5-10 keV interval. Our work is based on a complete
characterization of the instrumental background and an accurate measurement of
the stray-light contamination and vignetting calibration. We find that the CXRB
spectrum in the 1.5-7 keV energy band can be equally well fitted by a single
power-law with photon index Gamma=1.47+/-0.07 or a single power-law with photon
index Gamma=1.41+/-0.06 and an exponential roll-off at 41 keV. The measured
flux in the 2-10 keV energy band is 2.18+/-0.13 E-11 erg/(cm2 s deg2) in the
2-10 keV band. Combining Swift-XRT with Swift-BAT (15-200 keV) we find that, in
the 1.5-200 keV band, the CXRB spectrum can be well described by two
smoothly-joined power laws with the energy break at 29.0+/-0.5 keV
corresponding to a nu F_nu peak located at 22.4+/-0.4 keV. Taking advantage of
both the Swift high energy instruments (XRT and BAT), we produce an analytical
description of the CXRB spectrum over a wide (1.5-200 keV) energy band. This
model is marginally consistent with the HEAO1 measurement (~10% higher at
energies higher than 20 keV, while it is significantly (30%) higher at low
energies (2-10 keV).Comment: Accepted for publication by A&A; 9 pages, 11 figures. Typo corrected
in units of Tab. 2; update Fig. 1