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