Second Leibniz cohomology group of twisted N = 2 superconformal algebra

In this paper, we obtain all the Leibniz 2-cocycles of the twisted N = 2 superconformal algebra ℒ, which determine its second Leibniz cohomology group.     

Mild hydrothermal preparation of a layered metal hydroxide salt with microtube/rod morphology

Microtubes/rods of the layered metal hydroxide salt compound Cd2(OH)3(DS).nH2O, where DS stands for dodecyl sulfate sandwiched between two adjacent inorganic sheets, have been synthesized for the first time through a mild hydrothermal reaction route. The microtubes/rods have a diameter of about 1 μm and a length ranging from several microns to 20 μm. The growth process of microtubes/rods under the experimental conditions employed follows a dissolution-recrystallization route.     

Twisted longitudinal index theorem for foliations and wrong way functoriality

For a Lie groupoid G with a twisting σ (a PU(H)-principal bundle over G), we use the (geometric) deformation quantization techniques supplied by Connes tangent groupoids to define an analytic index morphism in twisted K-theory. In the case the twisting is trivial we recover the analytic index morphism of the groupoid.For a smooth foliated manifold with twistings on the holonomy groupoid we prove the twisted analog of the Connes–Skandalis longitudinal index theorem. When the foliation is given by fibers of a fibration, our index coincides with the one recently introduced by Mathai, Melrose, and Singer.We construct the pushforward map in twisted K-theory associated to any smooth (generalized) map f:W→M/F and a twisting σ on the holonomy groupoid M/F, next we use the longitudinal index theorem to prove the functoriality of this construction. We generalize in this way the wrong way functoriality results of Connes and Skandalis when the twisting is trivial and of Carey and Wang for manifolds.     

Invariant bilinear forms on real irreducible representations of real semisimple lie algebras *

In this note, we give a necessary and sufficient condition for a real irreducible representation of a real simple Lie algebra to admit an invariant bilinear form. We also determine when the invariant bilinear form is symmetric or skew-symmetric.     

Projective modules over noncommutative tori are multi-window Gabor frames for modulation spaces

In the present investigation we link noncommutative geometry over noncommutative tori with Gabor analysis, where the first has its roots in operator algebras and the second in time-frequency analysis. We are therefore in the position to invoke modern methods of operator algebras, e.g. topological stable rank of Banach algebras, to display the deeper properties of Gabor frames. Furthermore, we are able to extend results due to Connes and Rieffel on projective modules over noncommutative tori to Banach algebras, which arise in a natural manner in Gabor analysis. The main goal of this investigation is twofold: (i) an interpretation of projective modules over noncommutative tori in terms of Gabor analysis and (ii) to show that the Morita-Rieffel equivalence between noncommutative tori is the natural framework for the duality theory of Gabor frames. More concretely, we interpret generators of projective modules over noncommutative tori as the Gabor atoms of multi-window Gabor frames for modulation spaces. Moreover, we show that this implies the existence of good multi-window Gabor frames for modulation spaces with Gabor atoms in e.g. Feichtinger's algebra or in Schwartz space.     

Triangular Matrix Representations of Rings of Generalized Power Series

Let R be a ring and S a cancellative and torsion-free monoid and 〈 a strict order on S. If either （S,≤） satisfies the condition that 0 ≤ s for all s ∈ S, or R is reduced, then the ring [[R^S,≤]] of the generalized power series with coefficients in R and exponents in S has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is [[R^S,≤]].     

交换Hopf代数扭余作用下的余代数的上同调

该文证明了若交换Hopf代数在余代数C上的扭余作用的coassociator是卷积可逆的,那么该扭余作用也是可逆的.在这种情形下,给出了余代数C的正则上同调的定义,并且证得每个可逆的扭余作用可以提升到H的系数属于C的一个三次正则上同调类,且扭余作用的obstruction是平凡的当且仅当该扭余作用对应着一个cleft余扩张.