Twisted Heisenberg-Virasoro Algebra Research Articles

Subsingular vectors in Verma modules, and tensor product of weight modules over the twisted Heisenberg-Virasoro algebra and W(2, 2) algebra

We show that subsingular vectors may exist in Verma modules over W(2, 2), and present the subquotient structure of these modules. We prove conditions for irreducibility of the tensor product of intermediate series module with a highest weight module. Relation to intertwining operators over vertex operator algebra associated with W(2, 2) is discussed. Also, we study the tensor product of intermediate series and a highest weight module over the twisted Heisenberg-Virasoro algebra, and present series of irreducible modules with infinite-dimensional weight spaces.

Lie bialgebra structures on the twisted Heisenberg–Virasoro algebra

In this paper we investigate Lie bialgebra structures on the twisted Heisenberg–Virasoro algebra. With the determination of certain Lie bialgebra structures on the Virasoro algebra, we determine certain structures on the twisted Heisenberg–Virasoro algebra. Moreover, some general and useful results are obtained. With our methods and results we also can easily determine certain structures on some Lie algebras related to the twisted Heisenberg–Virasoro algebra.

Irreducible modules over the Virasoro algebra

In this paper, we construct two different classes of Virasoro modules from twisting Harish-Chandra modules over the twisted Heisenberg-Virasoro algebra by an automorphism of the twisted Heisenberg-Virasoro algebra. Weight modules in the first class are some irreducible highest weight modules over the twisted Heisenberg-Virasoro algebra. The non-weight modules in the first class are irreducible Whittaker modules over the Virasoro algebra. We obtain concrete bases for all irreducible Whittaker modules (instead of a quotient of modules). This generalizes known results on Whittaker modules. The second class of modules are non-weight modules which are not Whittaker modules. We determine the irreducibility and isomorphism classes of these modules.

CLASSIFICATION OF IRREDUCIBLE WEIGHT MODULES OVER THE TWISTED HEISENBERG–VIRASORO ALGEBRA

In this paper, all irreducible weight modules with finite dimensional weight spaces over the twisted Heisenberg–Virasoro algebra are determined. There are two different classes of them. One class is formed by simple modules of intermediate series, whose nonzero weight spaces are all 1-dimensional; the other class consists of the irreducible highest weight modules and lowest weight modules.

Whittaker modules for the twisted Heisenberg–Virasoro algebra

We define Whittaker modules for the twisted Heisenberg–Virasoro algebra and obtain several results from the classical setting, including a classification of simple Whittaker modules by central characters.

Harish-Chandra modules over the twisted Heisenberg-Virasoro algebra

In this paper, we classify all indecomposable Harish-Chandra modules of the intermediate series over the twisted Heisenberg-Virasoro algebra. Meanwhile, some bosonic modules are also studied.

Representations of the Twisted Heisenberg–Virasoro Algebra and the Full Toroidal Lie Algebras

An explicit construction of indecomposable modules for the twisted Heisenberg–Virasoro algebra and representations for the full toroidal Lie algebras are given.

The Derivation Algebra and Automorphism Group of the Twisted Heisenberg–Virasoro Algebra

In this article, we give the derivation algebra Der ℒ and the automorphism group Aut ℒ of the twisted Heisenberg–Virasoro algebra ℒ.

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 Heisenberg–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).

Euler-Poincaré Formalism of Coupled KdV Type Systems and Diffeomorphism Group on S1

This paper describes a wide class of coupled KdV equations. The first set of equations directly follow from the geodesic flows on the Bott-Virasoro group with a complex field. But the set of 2-component systems of nonlinear evolution equations, which includes dispersive water waves, Ito's equation, many other known and unknown equations, follow from the geodesic flows of the right invariant L 2 metric on the semidirect product group , where Diff( S 1 ) is the group of orientation preserving diffeomorphisms on a circle. We compute the Lie-Poisson brackets of the Antonowicz-Fordy system, and the mode expansion of these beackets yield the twisted Heisenberg-Virasoro algebra. We also give an outline to study geodesic flows of a H 1 metric on .

Representations of the Twisted Heisenberg–Virasoro Algebra at Level Zero

AbstractWe describe the structure of the irreducible highest weight modules for the twisted Heisenberg–Virasoro Lie algebra at level zero. We prove that either a Verma module is irreducible or its maximal submodule is cyclic.