67 research outputs found
The exactness of a general Skoda complex
We show that a Skoda complex with a general plurisubharmonic weight function
is exact if its 'degree' is sufficiently large. This answers a question of
Lazarsfeld and implies that not every integrally closed ideal is equal to a
multiplier ideal even if we allow general plurisubharmonic weights for the
multiplier ideal, extending the result of Lazarsfeld and Lee \cite{LL}.Comment: References added, exposition streamlined, to appear in Michigan
Mathematical Journa
From Koszul duality to Poincar\'e duality
We discuss the notion of Poincar\'e duality for graded algebras and its
connections with the Koszul duality for quadratic Koszul algebras. The
relevance of the Poincar\'e duality is pointed out for the existence of twisted
potentials associated to Koszul algebras as well as for the extraction of a
good generalization of Lie algebras among the quadratic-linear algebras.Comment: Dedicated to Raymond Stora. 27 page
Towards Spinfoam Cosmology
We compute the transition amplitude between coherent quantum-states of
geometry peaked on homogeneous isotropic metrics. We use the holomorphic
representations of loop quantum gravity and the
Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at
first order in the vertex expansion, second order in the graph (multipole)
expansion, and first order in 1/volume. We show that the resulting amplitude is
in the kernel of a differential operator whose classical limit is the canonical
hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an
indication that the dynamics of loop quantum gravity defined by the new vertex
yields the Friedmann equation in the appropriate limit.Comment: 8 page
Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
We classify Nichols algebras of irreducible Yetter-Drinfeld modules over
groups such that the underlying rack is braided and the homogeneous component
of degree three of the Nichols algebra satisfies a given inequality. This
assumption turns out to be equivalent to a factorization assumption on the
Hilbert series. Besides the known Nichols algebras we obtain a new example. Our
method is based on a combinatorial invariant of the Hurwitz orbits with respect
to the action of the braid group on three strands.Comment: v2: 35 pages, 6 tables, 14 figure
Closedness of star products and cohomologies
We first review the introduction of star products in connection with
deformations of Poisson brackets and the various cohomologies that are related
to them. Then we concentrate on what we have called ``closed star products" and
their relations with cyclic cohomology and index theorems. Finally we shall
explain how quantum groups, especially in their recent topological form, are in
essence examples of star products.Comment: 16 page
S^3/Z_n partition function and dualities
We investigate S^3/Z_n partition function of N = 2 supersymmetric gauge
theories. A gauge theory on the orbifold has degenerate vacua specified by the
holonomy. The partition function is obtained by summing up the contributions of
saddle points with different holonomies. An appropriate choice of the phase of
each contribution is essential to obtain the partition function. We determine
the relative phases in the holonomy sum in a few examples by using duality to
non-gauge theories. In the case of odd n the phase factors can be absorbed by
modifying a single function appearing in the partition function.Comment: 30 pages, 2 figures, added reference
Hodge Star as Braided Fourier Transform
We study super-braided Hopf algebras primitively generated by
finite-dimensional right crossed (or Drinfeld-Radford-Yetter) modules
over a Hopf algebra which are quotients of the augmentation
ideal under right multiplication and the adjoint coaction. Here
super-bosonisation provides a bicovariant differential
graded algebra on . We introduce providing the maximal
prolongation, while the canonical braided-exterior algebra
provides the Woronowicz exterior calculus. In
this context we introduce a Hodge star operator by super-braided
Fourier transform on and left and right interior products by
braided partial derivatives. Our new approach to the Hodge star (a) differs
from previous approaches in that it is canonically determined by the
differential calculus and (b) differs on key examples, having order 3 in middle
degree on with its 3D calculus and obeying the -Hecke relation
in middle degree on with its 4D
calculus. Our work also provided a Hodge map on quantum plane calculi and a new
starting point for calculi on coquasitriangular Hopf algebras whereby any
subcoalgebra defines a sub braided-Lie algebra and
provides the required data .Comment: 36 pages latex 4 pdf figures; minor revision; added some background
in calculus on quantum plane; improved the intro clarit
Molecular and cellular mechanisms underlying the evolution of form and function in the amniote jaw.
The amniote jaw complex is a remarkable amalgamation of derivatives from distinct embryonic cell lineages. During development, the cells in these lineages experience concerted movements, migrations, and signaling interactions that take them from their initial origins to their final destinations and imbue their derivatives with aspects of form including their axial orientation, anatomical identity, size, and shape. Perturbations along the way can produce defects and disease, but also generate the variation necessary for jaw evolution and adaptation. We focus on molecular and cellular mechanisms that regulate form in the amniote jaw complex, and that enable structural and functional integration. Special emphasis is placed on the role of cranial neural crest mesenchyme (NCM) during the species-specific patterning of bone, cartilage, tendon, muscle, and other jaw tissues. We also address the effects of biomechanical forces during jaw development and discuss ways in which certain molecular and cellular responses add adaptive and evolutionary plasticity to jaw morphology. Overall, we highlight how variation in molecular and cellular programs can promote the phenomenal diversity and functional morphology achieved during amniote jaw evolution or lead to the range of jaw defects and disease that affect the human condition
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