126 research outputs found
Generalized diagonal crossed products and smash products for quasi-Hopf algebras. Applications
In this paper we introduce generalizations of diagonal crossed products,
two-sided crossed products and two-sided smash products, for a quasi-Hopf
algebra H. The results we obtain may be applied to H^*-Hopf bimodules and
generalized Yetter-Drinfeld modules. The generality of our situation entails
that the "generating matrix" formalism cannot be used, forcing us to use a
different approach. This pays off because as an application we obtain an easy
conceptual proof of an important but very technical result of Hausser and Nill
concerning iterated two-sided crossed products.Comment: 41 pages, no figure
Tannaka-Krein duality for Hopf algebroids
We develop the Tannaka-Krein duality for monoidal functors with target in the
categories of bimodules over a ring. The \coend of such a functor turns out
to be a Hopf algebroid over this ring. Using the result of a previous paper we
characterize a small abelian, locally finite rigid monoidal category as the
category of rigid comodules over a transitive Hopf algebroid.Comment: 25 pages, final version, to appear in Israel Journal of Mathematic
On the trace of the antipode and higher indicators
We introduce two kinds of gauge invariants for any finite-dimensional Hopf
algebra H. When H is semisimple over C, these invariants are respectively, the
trace of the map induced by the antipode on the endomorphism ring of a
self-dual simple module, and the higher Frobenius-Schur indicators of the
regular representation. We further study the values of these higher indicators
in the context of complex semisimple quasi-Hopf algebras H. We prove that these
indicators are non-negative provided the module category over H is modular, and
that for a prime p, the p-th indicator is equal to 1 if, and only if, p is a
factor of dim H. As an application, we show the existence of a non-trivial
self-dual simple H-module with bounded dimension which is determined by the
value of the second indicator.Comment: additional references, fixed some typos, minor additions including a
questions and some remark
Hopf Categories
We introduce Hopf categories enriched over braided monoidal categories. The
notion is linked to several recently developed notions in Hopf algebra theory,
such as Hopf group (co)algebras, weak Hopf algebras and duoidal categories. We
generalize the fundamental theorem for Hopf modules and some of its
applications to Hopf categories.Comment: 47 pages; final version to appear in Algebras and Representation
Theor
Rigidity and defect actions in Landau-Ginzburg models
Studying two-dimensional field theories in the presence of defect lines
naturally gives rise to monoidal categories: their objects are the different
(topological) defect conditions, their morphisms are junction fields, and their
tensor product describes the fusion of defects. These categories should be
equipped with a duality operation corresponding to reversing the orientation of
the defect line, providing a rigid and pivotal structure. We make this
structure explicit in topological Landau-Ginzburg models with potential x^d,
where defects are described by matrix factorisations of x^d-y^d. The duality
allows to compute an action of defects on bulk fields, which we compare to the
corresponding N=2 conformal field theories. We find that the two actions differ
by phases.Comment: 53 pages; v2: clarified exposition of pivotal structures, corrected
proof of theorem 2.13, added remark 3.9; version to appear in CM
Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra
We rederive a popular nonsemisimple fusion algebra in the braided context,
from a Nichols algebra. Together with the decomposition that we find for the
product of simple Yetter-Drinfeld modules, this strongly suggests that the
relevant Nichols algebra furnishes an equivalence with the triplet W-algebra in
the (p,1) logarithmic models of conformal field theory. For this, the category
of Yetter-Drinfeld modules is to be regarded as an \textit{entwined} category
(the one with monodromy, but not with braiding).Comment: 36 pages, amsart++, times, xy. V3: references added, an unnecessary
assumption removed, plus some minor change
Vergleich von Lisinopril und Captopril zur Behandlung der schweren Herzinsuffizienz (NYHA III-IV) bei Hochrisikopatienten. Vorläufige Studienergebnisse (=Comparison of lisinopril and captopril in treatment of severe heart failure (NYHA III-IV) in high risk patients. Preliminary results of the trial)
We present preliminary data of a study comparing captopril, a short acting, with lisinopril, a long acting ACE-inhibitor in 8 of 12 projected patients with severe chronic heart failure (NYHA III-IV) and one additional risk factor (e.g. diabetes mellitus, renal failure). The 8 patients were treated in a cross over design for 12 weeks with either drug. While lisinopril improved NYHA-class in all patients, captopril reached this goal in only 3. Renal function was stable in all patients. Captopril influenced hormones (renin, aldosterone, norepinephrine, epinephrine) and microalbuminuria less than lisinopril. The number of adverse reactions was smaller in lisinopril treated patients. These preliminary data demonstrate at least an equal efficacy of lisinopril compared to captopril in high risk patients with severe chronic heart failure
Isospin-tracing: A probe of non-equilibrium in central heavy-ion collisions
Four different combinations of Ru and Zr nuclei, both
as projectile and target, were investigated at the same bombarding energy of
400 MeV using a detector. The degree of isospin mixing between
projectile and target nucleons is mapped across a large portion of the phase
space using two different isospin-tracer observables, the number of measured
protons and the yield ratio. The experimental results
show that the global equilibrium is not reached even in the most central
collisions. Quantitative measures of stopping and mixing are extracted from the
data. They are found to exhibit a quite strong sensitivity to the in-medium
(n,n) cross section used in microscopic transport calculations.Comment: 4 pages RevTeX, 3 figures (ps files), submitted to Phys. Rev. Let
Identification of baryon resonances in central heavy-ion collisions at energies between 1 and 2 AGeV
The mass distributions of baryon resonances populated in near-central
collisions of Au on Au and Ni on Ni are deduced by defolding the spectra
of charged pions by a method which does not depend on a specific resonance
shape. In addition the mass distributions of resonances are obtained from the
invariant masses of pairs. With both methods the deduced mass
distributions are shifted by an average value of -60 MeV/c relative to the
mass distribution of the free resonance, the distributions
descent almost exponentially towards mass values of 2000 MeV/c^2. The observed
differences between and pairs indicate a contribution
of isospin resonances. The attempt to consistently describe the
deduced mass distributions and the reconstructed kinetic energy spectra of the
resonances leads to new insights about the freeze out conditions, i.e. to
rather low temperatures and large expansion velocities.Comment: 30 pages, 13 figures, Latex using documentstyle[12pt,a4,epsfig], to
appear in Eur. Phys. J.
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