New types of bialgebras arising from the Hopf equation

New types of bialgebras arising from the Hopf equation (pentagonal equation) are introduced and studied. They will play from the Hopf equation the same role as the co-quasitriangular do from the quantum Yang Baxter equation.Comment: Latex2e, Comm Algebra, in pres

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 Pimsner–Voiculescu 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 Baum–Connes conjecture to the framework of discrete quantum groups. This is based on the categorical reformulation of the Baum–Connes conjecture developed by Meyer and Nest. As a main result we show that free quantum groups have a γ -element and that γ=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 Baum–Connes conjecture to our setting

MAT-756: INVESTIGATION OF THE IMPACT OF RAP GRADATION ON THE EFFECTIVE BINDER CONTENT IN HOT MIX ASPHALT

Nowadays, it is common to add a little amount of Reclaimed Asphalt Pavement (RAP) in asphalt mixes without changing too much properties such as modulus and low temperature cracking resistance. Not only will those mixes be able to make roads last longer, but they will be a greener alternative to usual mixes. In order to make a flexible pavement design, the mixture behavior is usually characterized with the complex modulus. To have a high modulus mix, you need to control the gradation precisely even when RAP is added. When performing a mix design to incorporate RAP, it is desirable to know the RAP binder characteristics and content and its gradation. In the literature, there is no clear vision of the RAP gradation impacts on the mixture properties and field performance. The objective of this study, performed at the Pavements and Bituminous Materials Laboratory (LCMB), is to evaluate the impact of RAP gradation on Hot Mix Asphalt. This is needed to understand how much binder can be transferred during mix from RAP to virgin aggregate. In this study, a single source of RAP was separated into different sizes and mixed with a specific group of virgin aggregates. Then, according to their size, the mixes were separated again into the RAP group and virgin aggregate. While these were mixed, active RAP binder transferred to virgin aggregate. Then ignition test (ASTM D6307) was adapted to separate RAP binder from virgin aggregate. With this procedure, it was possible to see that, for a given temperature and mixing time, activated binder amount of coarse RAP particles and fine RAP particles. The Ignition test result showed that coarse RAP particles have more active binder in mix but ITS test indicated that fine RAP particles have higher strength

On globally non-trivial almost-commutative manifolds

Within the framework of Connes' noncommutative geometry, we define and study globally non-trivial (or topologically non-trivial) almost-commutative manifolds. In particular, we focus on those almost-commutative manifolds that lead to a description of a (classical) gauge theory on the underlying base manifold. Such an almost-commutative manifold is described in terms of a 'principal module', which we build from a principal fibre bundle and a finite spectral triple. We also define the purely algebraic notion of 'gauge modules', and show that this yields a proper subclass of the principal modules. We describe how a principal module leads to the description of a gauge theory, and we provide two basic yet illustrative examples.Comment: 34 pages, minor revision

Bicrossproduct approach to the Connes-Moscovici Hopf algebra

We give a rigorous proof that the (codimension one) Connes-Moscovici Hopf algebra H_CM is isomorphic to a bicrossproduct Hopf algebra linked to a group factorisation of the group of positively-oriented diffeomorphisms of the real line. We construct a second bicrossproduct U_CM equipped with a nondegenerate dual pairing with H_CM. We give a natural quotient Hopf algebra of H_CM and Hopf subalgebra of U_CM which again are in duality. All these Hopf algebras arise as deformations of commutative or cocommutative Hopf algebras that we describe in each case. Finally we develop the noncommutative differential geometry of the quotient of H_CM by studying covariant first order differential calculi of small dimension over this algebra.Comment: 21 page

Noncommutative elliptic theory. Examples

We study differential operators, whose coefficients define noncommutative algebras. As algebra of coefficients, we consider crossed products, corresponding to action of a discrete group on a smooth manifold. We give index formulas for Euler, signature and Dirac operators twisted by projections over the crossed product. Index of Connes operators on the noncommutative torus is computed.Comment: 23 pages, 1 figur

The Hopf modules category and the Hopf equation

We study the Hopf equation which is equivalent to the pentagonal equation, from operator algebras. A FRT type theorem is given and new types of quantum groups are constructed. The key role is played now by the classical Hopf modules category. As an application, a five dimensional noncommutative noncocommutative bialgebra is given.Comment: 30 pages, Letax2e, Comm. Algebra in pres

Quantum Field Theory on the Noncommutative Plane with Eq(2)E_q(2) Symmetry

We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we define quantum fields depending on noncommutative coordinates and construct a field theoretical action using the $E_q(2)$-invariant measure on the noncommutative plane. With the help of the partial wave decomposition we show that this quantum field theory can be considered as a second quantization of the particle theory on the noncommutative plane and that this field theory has (contrary to the common belief) even more severe ultraviolet divergences than its counterpart on the usual commutative plane. Finally, we introduce the symmetry transformations of physical states on noncommutative spaces and discuss them in detail for the case of the $E_q(2)$ quantum group.Comment: LaTeX, 26 page

Equivariant comparison of quantum homogeneous spaces

We prove the deformation invariance of the quantum homogeneous spaces of the q-deformation of simply connected simple compact Lie groups over the Poisson-Lie quantum subgroups, in the equivariant KK-theory with respect to the translation action by maximal tori. This extends a result of Neshveyev-Tuset to the equivariant setting. As applications, we prove the ring isomorphism of the K-group of Gq with respect to the coproduct of C(Gq), and an analogue of the Borsuk-Ulam theorem for quantum spheres.Comment: 21 page

Overview of the Role of 308 Monochromatic Excimer Phototherapy for the Treatment of Alopecia Areata

Treatment of alopecia areata (AA) remains challenging despite the advancement in all these years. Excimer phototherapy has been claimed to offer a practical alternative therapeutic option without significant risks. It is considered a “super-narrowband” UVB light source that emits energy at 308 nm. Excimer laser treatment achieves a remarkable effect in T cell-mediated disorders; thus, it has been used successfully in patients with AA. Compared with narrowband UVB, the excimer laser can induce apoptosis in vitro, paralleled by improved clinical efficacy. Both excimer laser and lamp have a similar effect, but they differ in technology. In this chapter, an evaluation of the effectiveness of 308 nm monochromatic excimer phototherapy in AA treatment is clinically warranted. The evidence-based studies that adopted this option using both laser and light are discussed. In addition, the formulation of therapeutic protocol to study the outcome of excimer treatment on moderate-to-severe AA in adults and children is described