26,123 research outputs found
Conversion of B-rep CAD models into globally G<sup>1</sup> triangular splines
Existing techniques that convert B-rep (boundary representation) patches into Clough-Tocher splines guarantee watertight, that is C0, conversion results across B-rep edges. In contrast, our approach ensures global tangent-plane, that is G1, continuity of the converted B-rep CAD models. We achieve this by careful boundary curve and normal vector management, and by converting the input models into Shirman-Séquin macro-elements near their (trimmed) B-rep edges. We propose several different variants and compare them with respect to their locality, visual quality, and difference with the input B-rep CAD model. Although the same global G1 continuity can also be achieved by conversion techniques based on subdivision surfaces, our approach uses triangular splines and thus enjoys full compatibility with CAD
A rigidity result for extensions of braided tensor C*-categories derived from compact matrix quantum groups
Let G be a classical compact Lie group and G_\mu the associated compact
matrix quantum group deformed by a positive parameter \mu (or a nonzero and
real \mu in the type A case). It is well known that the category Rep(G_\mu) of
unitary f.d. representations of G_\mu is a braided tensor C*-category. We show
that any braided tensor *-functor from Rep(G_\mu) to another braided tensor
C*-category with irreducible tensor unit is full if |\mu|\neq 1. In particular,
the functor of restriction to the representation category of a proper compact
quantum subgroup, cannot be made into a braided functor. Our result also shows
that the Temperley--Lieb category generated by an object of dimension >2 can
not be embedded properly into a larger category with the same objects as a
braided tensor C*-subcategory.Comment: 19 pages; published version, to appear in CMP; for a more detailed
exposition see v
How to add a boundary condition
Given a conformal QFT local net of von Neumann algebras B_2 on the
two-dimensional Minkowski spacetime with irreducible subnet A\otimes\A, where A
is a completely rational net on the left/right light-ray, we show how to
consistently add a boundary to B_2: we provide a procedure to construct a
Boundary CFT net B of von Neumann algebras on the half-plane x>0, associated
with A, and locally isomorphic to B_2. All such locally isomorphic Boundary CFT
nets arise in this way. There are only finitely many locally isomorphic
Boundary CFT nets and we get them all together. In essence, we show how to
directly redefine the C* representation of the restriction of B_2 to the
half-plane by means of subfactors and local conformal nets of von Neumann
algebras on S^1.Comment: 20 page
On the representation theory of Virasoro Nets
We discuss various aspects of the representation theory of the local nets of
von Neumann algebras on the circle associated with positive energy
representations of the Virasoro algebra (Virasoro nets). In particular we
classify the local extensions of the Virasoro net for which the
restriction of the vacuum representation to the Virasoro subnet is a direct sum
of irreducible subrepresentations with finite statistical dimension (local
extensions of compact type). Moreover we prove that if the central charge
is in a certain subset of , including , and , the irreducible representation with lowest weight of the
corresponding Virasoro net has infinite statistical dimension. As a consequence
we show that if the central charge is in the above set and satisfies then the corresponding Virasoro net has no proper local extensions of
compact type.Comment: 34 page
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