On indecomposable modules over the Virasoro algebra

It is proved that an indecomposable Harish-Chandra module over the Virasoro algebra must be (i) a uniformly bounded module, or (ii) a module in Category $\cal O$, or (iii) a module in Category ${\cal O}^-$, or (iv) a module which contains the trivial module as one of its composition factors.Comment: 5 pages, Latex, to appear in Science in China

Spin transfer in a ferromagnet-quantum dot and tunnel barrier coupled Aharonov-Bohm ring system with Rashba spin-orbit interactions

The spin transfer effect in ferromagnet-quantum dot (insulator)-ferromagnet Aharonov-Bohm (AB) ring system with Rashba spin-orbit (SO) interactions is investigated by means of Keldysh nonequilibrium Green function method. It is found that both the magnitude and direction of the spin transfer torque (STT) acting on the right ferromagnet electrode can be effectively controlled by changing the magnetic flux threading the AB ring or the gate voltage on the quantum dot. The STT can be greatly augmented by matching a proper magnetic flux and an SO interaction at a cost of low electrical current. The STT, electrical current, and spin current are uncovered to oscillate with the magnetic flux. The present results are expected to be useful for information storage in nanospintronics.Comment: 17pages, 7figure

Classification of irreducible quasifinite modules over map Virasoro algebras

We give a complete classification of the irreducible quasifinite modules for algebras of the form Vir \otimes A, where Vir is the Virasoro algebra and A is a Noetherian commutative associative unital algebra over the complex numbers. It is shown that all such modules are tensor products of generalized evaluation modules. We also give an explicit sufficient condition for a Verma module of Vir \otimes A to be reducible. In the case that A is an infinite-dimensional integral domain, this condition is also necessary.Comment: 25 pages. v2: Minor changes, published versio

Lie bialgebras of generalized Witt type

In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are classified. It is proved that, for any Lie algebra $W$ of generalized Witt type, all Lie bialgebras on $W$ are coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group $H^1(W,W \otimes W)$ is trivial.Comment: 14 page

Common Warm Dust Temperatures Around Main-sequence Stars

We compare the properties of warm dust emission from a sample of main-sequence A-type stars (B8-A7) to those of dust around solar-type stars (F5-K0) with similar Spitzer Space Telescope Infrared Spectrograph/MIPS data and similar ages. Both samples include stars with sources with infrared spectral energy distributions that show evidence of multiple components. Over the range of stellar types considered, we obtain nearly the same characteristic dust temperatures (~190 K and ~60 K for the inner and outer dust components, respectively)—slightly above the ice evaporation temperature for the inner belts. The warm inner dust temperature is readily explained if populations of small grains are being released by sublimation of ice from icy planetesimals. Evaporation of low-eccentricity icy bodies at ~150 K can deposit particles into an inner/warm belt, where the small grains are heated to T_(dust)~ 190 K. Alternatively, enhanced collisional processing of an asteroid belt-like system of parent planetesimals just interior to the snow line may account for the observed uniformity in dust temperature. The similarity in temperature of the warmer dust across our B8-K0 stellar sample strongly suggests that dust-producing planetesimals are not found at similar radial locations around all stars, but that dust production is favored at a characteristic temperature horizon