K\"ahlerian Twistor Spinors

On a K\"ahler spin manifold K\"ahlerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the K\"ahler structure, called K\"ahlerian twistor (Penrose) operator. We study K\"ahlerian twistor spinors and give a complete description of compact K\"ahler manifolds of constant scalar curvature admitting such spinors. As in the Riemannian case, the existence of K\"ahlerian twistor spinors is related to the lower bound of the spectrum of the Dirac operator.Comment: shorter version; to appear in Math.

The Secondary Transition Planning Process and Effective Outcomes for High School Graduates with Mild Disabilities

The secondary transition planning process and effective outcomes for high school graduates with mild disabilities

Regeneration of Cellulose from a Switchable Ionic Liquid: Toward More Sustainable Cellulose Fibers

A CO$_{2}$ switchable solvent system is investigated to find an environmentally friendlier way to produce man‐made cellulose fibers. Cellulose solutions with concentrations from 2 wt% to 8 wt%, based on derivative and non‐derivative dissolution approaches, are investigated. Three different switchable solvent systems are tested. After accessing the stability of the produced cellulose solutions, their regeneration is investigated using different alcoholic coagulation media. In order to find a suitable coagulation medium and stable cellulose solution, a dissolution–regeneration cycle is investigated, while trying to minimize the amount of waste by recovering the employed solvents. The process is optimized and the resulting fibers are characterized by infrared (IR) spectroscopy, optical microscopy, as well as scanning electron microscopy

Symmetries of N=4 supersymmetric CP(n) mechanics

We explicitly constructed the generators of $SU(n+1)$ group which commute with the supercharges of N=4 supersymmetric $\mathbb{CP}^n$ mechanics in the background U(n) gauge fields. The corresponding Hamiltonian can be represented as a direct sum of two Casimir operators: one Casimir operator on $SU(n+1)$ group contains our bosonic and fermionic coordinates and momenta, while the second one, on the SU(1,n) group, is constructed from isospin degrees of freedom only.Comment: 10 pages, PACS numbers: 11.30.Pb, 03.65.-w; minor changes in Introduction, references adde

A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself

We give an example of an exact, stably finite, simple. separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank zero and stable rank one, has a unique tracial state, and the order on projections over D is determined by traces. It also absorbs the Jiang-Su algebra Z, and in fact absorbs the 3^{\infty} UHF algebra. We can also explicitly compute the K-theory of D, namely K_0 (D) = Z[1/3] with the standard order, and K_1 (D) = 0, as well as the Cuntz semigroup of D.Comment: 16 pages; AMSLaTeX. The material on other possible K-groups for such an algebra has been moved to a separate paper (1309.4142 [math.OA]

From the Dirac Operator to Wess-Zumino Models on Spatial Lattices

We investigate two-dimensional Wess-Zumino models in the continuum and on spatial lattices in detail. We show that a non-antisymmetric lattice derivative not only excludes chiral fermions but in addition introduces supersymmetry breaking lattice artifacts. We study the nonlocal and antisymmetric SLAC derivative which allows for chiral fermions without doublers and minimizes those artifacts. The supercharges of the lattice Wess-Zumino models are obtained by dimensional reduction of Dirac operators in high-dimensional spaces. The normalizable zero modes of the models with N=1 and N=2 supersymmetry are counted and constructed in the weak- and strong-coupling limits. Together with known methods from operator theory this gives us complete control of the zero mode sector of these theories for arbitrary coupling.Comment: 39 pages, 3 figure

Extended Supersymmetries and the Dirac Operator

We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges that exist and restrictions on the geometry of the underlying spaces as well as the admissible gauge field configurations. From the superalgebra with two or more real supercharges we infer the existence of integrability conditions and obtain a corresponding superpotential. This potential can be used to deform the supercharges and to determine zero modes of the Dirac operator. The general results are applied to the Kahler spaces CP^n.Comment: 22 pages, no figure

Relative commutants of strongly self-absorbing C*-algebras

The relative commutant $A'\cap A^{\mathcal{U}}$ of a strongly self-absorbing algebra $A$ is indistinguishable from its ultrapower $A^{\mathcal{U}}$. This applies both to the case when $A$ is the hyperfinite II$_1$ factor and to the case when it is a strongly self-absorbing C*-algebra. In the latter case we prove analogous results for $\ell_\infty(A)/c_0(A)$ and reduced powers corresponding to other filters on $\bf N$. Examples of algebras with approximately inner flip and approximately inner half-flip are provided, showing the optimality of our results. We also prove that strongly self-absorbing algebras are smoothly classifiable, unlike the algebras with approximately inner half-flip.Comment: Some minor correction

Locally Trivial W*-Bundles

We prove that a tracially continuous W$^*$-bundle $\mathcal{M}$ over a compact Hausdorff space $X$ with all fibres isomorphic to the hyperfinite II$_1$-factor $\mathcal{R}$ that is locally trivial already has to be globally trivial. The proof uses the contractibility of the automorphism group $\mathrm{Aut}({\mathcal{R}})$ shown by Popa and Takesaki. There is no restriction on the covering dimension of $X$.Comment: 20 pages, this version will be published in the International Journal of Mathematic