37,933 research outputs found
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
, or (iii) a module in Category , 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 of generalized Witt type, all Lie bialgebras on are
coboundary triangular Lie bialgebras. As a by-product, it is also proved that
the first cohomology group is trivial.Comment: 14 page
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