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.

Kac Determinant Formula for the q-deformed Virasoro Algebra of Hom-type

We investigate the highest weight representations of the q-deformed Virasoro algebra of Hom-type. In order to determine its unitarity and irreducible highest weight representations, we present its Kac determinant formula when q is nonzero and non-root of unity.

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.

DERIVATION ALGEBRAS OF THE MODULAR LIE SUPERALGEBRAS W AND S OF CARTAN-TYPE

Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.

The Derivation Algebra of Qn Filiform Lie Algebra

In this paper, we explicitly determine the maximal torus of the derivation algebra of a Qn filiform Lie algebra. Using the root space decomposition of DerQn, we prove that the derivation algebra of a Qn filiform Lie algebra is complete.

Derivation Algebra of Quasi R_n-filiform Lie Algebra

In this paper we explicitly determine the derivation algebra of a quasi Rn-filiform Lie algebra and prove that a quasi Rn-filiform Lie algebra is a completable nilpotent Lie algebra.

The Derivation Algebra of the Cartan-type Lie Superalgebra H

In this paper, the derivation algebra of Lie superalgebra H of Caftan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following： DerFH = adH（H＂ ＋ Fh） （{（adDi）^pt ｜ i = 1,2,…,m, t=1,2,…,ti-1}）.

Derivations and Automorphism Group of Original Deformative Schrodinger-Virasoro Algebra

In this paper, we determine the derivation algebra and the automorphism group of the original deformative Schrodinger-Virasoro algebra, which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module Ig（a, b）.

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 submodu]e of the regular module.

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.

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）.

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 $O$ , or (iii) a module in Category $O$ , or ( iv) a module which contains the trivial module as one of its composition factors.

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.

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.

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.

Derivations and 2-Local Derivations on the BMS-Weyl Algebra

Using the theory of derivations on finitely generated and graded Lie algebras, we determine that derivations of the BMS-Weyl algebra are all inner. On this basis, it is proved that every 2-local derivation of the BMS-Weyl algebra is a derivation.

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.