1,721,403 research outputs found
Hopf C*-algebras
Full text linkIn this paper we introduce the notion of a Hopf C*-algebra and construct the
counit and antipode. A Hopf C*-algebra is a C*-algebra with comultiplication
satisfying some extra condition which makes possible the construction of the
counit and antipode. The leading example is of course the C*-algebra of
continuous, vanishing at infinity functions on a locally compact group. Also
locally compact quantum groups will be examples. We include several formulas
for the counit and antipode which are familiar from Hopf algebra theory.status: Publishe
Yetter-Drinfel'd algebras and coideals of Weak Hopf C * -Algebras
No full text46 pages, 30 ref.International audienceWe characterize braided commutative Yetter-Drinfeld C *-algebras over weak Hopf C *-algebras in categorical terms. Using this, we then study quotient type coideal subalgebras of a given weak Hopf C *-algebra G and coideal subalgebras invariant with respect to the adjoint action of G. Finally, as an example, we explicitly describe quotient type coideal subalgebras of the weak Hopf C *-algebras associated with Tambara-Yamagami categories
Classifying (Weak) Coideal Subalgebras of Weak Hopf C ¦ -Algebras
No full textInternational audienceWe develop a general approach to the problem of classification of weak coideal C ¦-subalgebras of weak Hopf C ¦-algebras. As an example, we consider weak Hopf C ¦-algebras and their weak coideal C ¦-subalgebras associated with Tambara Yamagami categories
Functional optimization for a Beam Driven Plasma Neutralizer in DEMO Neutral Beam Injector
Full text linkThe Beam Driven Plasma Neutralizer (BDPN) has been proposed as a more efficient alternative to the gas neutralizer for negative-ion based Neutral Beam Injection (NNBI). In this paper we model the performance of an entire NNBI beamline with a BDPN. We simultaneously consider all the relevant physics and engineering aspects, the most important being the plasma density and degree of ionization inside the BDPN as a function of its geometry and feed gas flow, the geometrical transmission of the beamline, the dependence of the neutral gas distribution in the beamline on the geometry of the beamline components and gas flows, and the species evolution of the extracted D− beam through this neutral and charged particle distribution. Furthermore, we calculate the heat loads expected on the BDPN parts and on the NBI components located downstream of it and study the effect of the magnetic cusp field across the BDPN entrance on beamline transmission. While our results constitute an optimization only under the applied boundary conditions, we find that the beamline with a BDPN increases the system’s wall plug efficiency by about 13% to 0.34 from the 0.30 estimated for a gas neutralizer
On finiteness of the N-dimensional Hopf C*-algebras
No full textInternational audienceGiven an algebraically closed field and an integer , D. \c Stefan has proved that there exists only a finite number of Hopf -algebras which are both semi-simple and co-semi-simple. In the C--algebraic framework, we provide in this note explicit upper-bounds for the number of Hopf C--algebra structures on a given finite dimensional C--algebra
Weak Hopf C∗-algebras and depth two subfactors
No full textAbstractWe prove that for a finite index and depth two inclusion N⊂M of II1 factors, the relative commutants N′∩M1 and M′∩M2 admit mutually dual weak Hopf C∗-algebra structures. The proof is based on ‘planar algebra techniques’. In the hyperfinite case, one can show that N′∩M1 acts on M with invariants N using this approach
Produktsysteme aus bikategorieller Sichtweise und Dualitätstheorie für Hopf C*-Algebren
No full textIn the first part of this doctoral thesis we want to take a look at
product systems from a new point of view and reveal the structure that
lies behind them using bicategory theory. After a short introduction
to bicategory theory, we show that Fowler's product systems are special
morphisms from a semigroup S to the bicategory C*ARR. Thus, we can give a
more elegant definition of the notion of a product system by defining
them as morphisms from an index category J to the bicategory C*ARR.
We will associate two C*-algebras to every given product system,
namely the corresponding reduced Toeplitz algebra and the corresponding
reduced Cuntz-Pimsner algebra. Studying various special cases shows that
our method of constructing the reduced Toeplitz and Cuntz-Pimsner algebras
generalizes many other constructions of C*-algebras. Moreover, we will
introduce the universal Toeplitz algebra and the universal Cuntz-Pimsner
algebra. We recall the notion of the bicategorial colimit for a morphism
and we show that for certain product systems the universal Toeplitz
algebra can be viewed as the bicategorial colimit object for this product
system.
In the second part of the thesis we develop a duality theory for locally
compact semigroups using the concept of Hopf C*-algebras, which can be
viewed as generalized locally compact semigroups. We develop a sufficient
condition on Hopf C*-algebras H that allows us to construct a corepresentation
of H on a distinguished Hilbert space. Using this regular corepresentation,
we can define the reduced dual C*-algebra of a Hopf C*-algebra. The duality
between these C*-algebras can be viewed as an analogue of Pontryagin's
duality theorem. Finally, we introduce the reduced crossed product of a
dynamical cosystem and treat an analogue of Takai's duality theorem for
crossed products by C*-arrows.Im ersten Teil dieser Doktorarbeit wollen wir Produktsysteme von
einem höheren Standpunkt aus betrachten und mit Hilfe der
Bikategorientheorie die Struktur offen legen, die sich hinter ihnen
verbirgt. Nach einer kurzen Einführung in die Bikategorientheorie
zeigen wir, dass es sich bei den Produktsystemen von Fowler um
spezielle Morphismen von einer Halbgruppe S in die Bikategorie
C*ARR handelt. Somit können wir eine natürlichere und elegantere
Definition für Produktsysteme angeben, indem wir definieren, dass
ein Produktsystem ein Morphismus von einer Indexkategorie J in die
Bikategorie C*ARR ist.
Wir ordnen jedem Produktsystem seine zugehörige reduzierte Toeplitz-
und seine zugehörige reduzierte Cuntz-Pimsner-Algebra zu. Desweiteren
untersuchen wir diverse Spezialfälle, die zeigen, dass unsere
Konstruktionsmethoden für die reduzierten Toeplitz- bzw. Cuntz-Pimsner-Algebren
viele andere Konstruktionen von C*-Algebren verallgemeinern. Anschließend
führen wir die universelle Toeplitz- und die universelle Cuntz-Pimsner-Algebra
ein. Wir wiederholen den Begriff des bikategoriellen Kolimes für
einen Morphismus und zeigen, dass für gewisse Produktsysteme die
zugehörige universelle Toeplitz-Algebra als das bikategorielle
Kolimesobjekt dieses Produktsystems betrachtet werden kann.
Im zweiten Teil der Arbeit entwickeln wir eine Dualitätstheorie
für lokalkompakte Halbgruppen und greifen dabei auf das Konzept
der Hopf C*-Algebren zurück, die man als verallgemeinerte
lokalkompakte Halbgruppen betrachten kann. Wir entwickeln eine
hinreichende Bedingung an die Hopf C*-Algebra H, die es uns
ermöglicht, eine Kodarstellung von H auf einem ausgezeichneten
Hilbertraum zu konstruieren. Mit Hilfe dieser regulären
Kodarstellung können wir dann die reduzierte duale C*-Algebra
einer Hopf C*-Algebra einführen. Die Dualität zwischen diesen
beiden C*-Algebren kann als Analogon zum Dualitätssatz von
Pontryagin betrachtet werden. Schließlich führen wir das
reduzierte verschränkte Produkt zu einem dynamischen Kosystem ein
und behandeln ein Analogon zum Dualitätssatz von Takai für
verschränkte Produkte durch C*-Pfeile
On finiteness of the N-dimensional Hopf C*-algebras
Full text linkInternational audienceGiven an algebraically closed field and an integer , D. \c Stefan has proved that there exists only a finite number of Hopf -algebras which are both semi-simple and co-semi-simple. In the C--algebraic framework, we provide in this note explicit upper-bounds for the number of Hopf C--algebra structures on a given finite dimensional C--algebra
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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