A NEW EXTENSION OF THE HIGH-ORDER VIRASORO ALGEBRA

This paper investigates the high order differential neighbourhoods of holomorphic mappings from S-1 x S-1 to a vector space and gives a new extension of the high-order Virasoro algebra.

LIE SUPER-BIALGEBRA STRUCTURES ON GENERALIZED SUPER-VIRASORO ALGEBRAS

In this article, Lie super-bialgebra structures on generalized super-Virasoro algebras/： are considered. It is proved that all such Lie super-bialgebras are coboundary triangular Lie super-bialgebras if and only if Hi（ ） = 0.

REPRESENTATIONS OF THE TWO PARAMETER DEFORMATION OF THE VIRASORO ALGEBRA

This paper constructs a class of Harish-Chandra modules with multiplicity≤1 of the two parameter deformation of Virasoro algebra and proves a classification theorem.

Lie Bialgebra Structures on Generalized Heisenberg-Virasoro Algebra

In a recent article by Liu,Pei,and Zhu,Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra were determined. By disposing the indexing set, the generalized Heisenberg-Virasoro algebra was considered. It is proved that all Lie bialgebra structures on centerless generalized Heisenberg-Virasoro algebra L are coboundary triangular by proving that the first cohomology group H1 (L,V) =0.

一类Heisenberg-Virasoro李代数上的交换线性映射

根据交换线性映射的性质,计算秩为2的Heisenberg-Virasoro李代数上的交换线性映射,以确定此李代数的形心.

超Heisenberg-Virasoro代数的Hom-李超代数结构

Hom-李超代数是由Hom-李代数的推广演化发展而来,Hom-李代数是一类同时满足反对称和HomJacobi等式的非结合代数。试图进一步确定超Heisenberg-Virasoro代数上的Hom-李超代数结构,证明超HeisenbergVirasoro代数上的Hom-李超代数结构是非平凡的。

Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over Twisted Heisenberg-Virasoro Algebra

We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenber-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module （and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series）.

Structures of Not-finitely Graded Lie Algebras Related to Generalized Heisenberg–Virasoro Algebras

In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.

Whittaker modules over loop Virasoro algebra

In this paper, we study Whittaker modules over the loop Virasoro algebra relative to some total order. We give a description of all Whittaker vectors for the universal Whittaker modules. We also show that any universal Whittaker module admits a unique simple quotient modules except for a special case.

Pointed Representations of Virasoro Algebra

In this paper we study the pointed representations of the Virasoro algebra.We show that unitary irreducible pointed representations of the Virasoro algebra are Harish-Chandra repre- sentations,thus they either are of highest or lowest weights or have all weight spaces of dimension 1.Further,we prove that unitary irreducible weight representations of Virasoro superalgebras are either of highest weights or of lowest weights,hence they are also Harish-Chandra representations.

The Restriction of Polynomial Modules for the Virasoro Algebra to sl_(2)(C)

The Lie algebra sl_(2)(C)may be regarded in a natural way as a subalgebra of the infinite-dimensional Virasoro Lie algebra,so it is natural to consider connections between the representation theory of the two algebras.In this paper,we explore the restriction to sl_(2)(C)of certain induced modules for the Virasoro algebra.Specifically,we consider Virasoro modules induced from so-called polynomial subalgebras,and we show that the restriction of these modules results in twisted versions of familiar modules such as Verma modules and Whittaker modules.

A Family of Non-weight Modules over the Virasoro Algebra

In this paper,we consider the tensor product modules of a class of non-weight modules and highest weight modules over the Virasoro algebra.We determine the necessary and sufficient conditions for such modules to be simple and the isomorphism classes among all these modules.Finally,we prove that these simple non-weight modules are new if the highest weight module over the Virasoro algebra is non-trivial.

Classification of simple weight modules for super-Virasoro algebra with a finite-dimensional weight space

There are two extensions of Virasoro algebra with particular importance in superstring theory： the Ramond algebra and the Neveu-Schwarz algebra, which are Z2-graded extensions of the Virasoro algebra. In this paper, we show that the support of a simple weight module over the Ramond algebra with an infinite-dimensional weight space coincides with the weight lattice and that all intersections of non-trivial weight spaces and odd part or even part of the module are infinite-dimensional. This result together with the one that we have obtained over the Neveu-Schwarz algebra generalizes the result for the Virasoro algebra to the super-Virasoro algebras.

Left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra

The compatible left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra with some natural grading conditions are completely determined.The results of the earlier work on left-symmetric algebra structures on the Virasoro algebra play an essential role in determining these compatible structures.As a corollary,any such left-symmetric algebra contains an infinite-dimensional nontrivial subalgebra that is also a submodule of the regular module.

Deformations on the Twisted Heisenberg-Virasoro Algebra

With the cohomology results on the Virasoro algebra, the authors determine the second cohomology group on the twisted Heisenberg-Virasoro algebra, which gives all deformations on the twisted Heisenberg-Virasoro algebra.

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.

Kac-Moody-Virasoro symmetry algebra of a (2+1)-dimensional bilinear system

Based on some known facts of integrable models, this paper proposes a new （2＋1）-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable because of the existence of the higher order symmetries. The Lie point symmetries of the model constitute an infinite dimensional Kac- Moody Virasoro symmetry algebra. Making use of the infinite Lie point symmetries, the possible symmetry reductions of the model are also studied

Lie Bialgebras of Generalized Loop Virasoro Algebras

The first cohomology group of generalized loop Virasoro algebras with coefficients in the tensor product of its adjoint module is shown to be trivial. The result is used to prove that Lie bialgebra structures on generalized loop Virasoro algebras are coboundary triangular. The authors generalize the results to generalized map Virasoro algebras.

Irreducible Weight Modules over the Twisted SchrSdinger-Virasoro Algebra

It is shown that the support of an irreducible weight module over the SchrSdinger-Virasoro Lie algebra with an infinite-dimensional weight space coincides with the weight lattice, and all nontrivial weight spaces of such a module are infinite-dimensional. As a by-product, it is obtained that every simple weight module over Lie algebra of this type with a nontrivial finite-dimensional weight space is a Harish-Chandra module.

Some conjectures on modular representations of affine sl_2 and Virasoro algebra

We conjecture an explicit bound on the prime characteristic of a field, under which the Weyl modules of affine sl_2 and the minimal series modules of Virasoro algebra remain irreducible, and Goddard-Kent-Olive coset construction for affine sl_2 is valid.