We show the OPE formulae for three types of deformed super-Virasoro algebras: Chaichian-Presnajder's deformation, Belov-Chaltikhian's one and its modified version. Fundamental (anti-)commutation relations toward a ghost realization of deformed super-Virasoro algebra are also discussed.

We study a class of infinite dimensional Lie algebras called generalized Witt algebras (in one variable). These include the classical Witt algebra and the centerless Virasoro algebra as important examples. We show that any such generalized Witt algebra is a semisimple, indecomposable Lie algebra which does not contain any abelian Lie subalgebras of dimension greater than one. We develop an inva...

A conformal vector with central charge c in a vertex operator algebra is an element of weight two whose component operators satisfy the Virasoro algebra relation with central charge c. Then the vertex operator subalgebra generated by the vector is isomorphic to a highest weight module for the Virasoro algebra with central charge c and highest weight 0 (cf. [M]). Let V2Al be the vertex operator ...

Abstract. In this paper, we study certain Virasoro frames for lattice vertex operator algebras and their Z2-orbifolds using linear codes over Z4. We also compute the corresponding frame stabilizer from the view point of binary codes and Z4-codes. As an application, we determine the frame stabilizers of several Virasoro frames of the vertex operator algebra VE8 and the moonshine vertex operator ...

We prove that the extended Toda hierarchy of [1] admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators Lm, m ≥ −1 of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination...

We prove that the extended Toda hierarchy of [1] admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators Lm, m ≥ −1 of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination...

We explicitly demonstrate that the unitary representations of the w ∞ algebra and its truncations are just the unitary representations of the Virasoro algebra.

An analog of the minimal unitary series representations for the deformed Virasoro algebra is constructed using vertex operators of the quantum affine algebra Uq(ŝl2). A similar construction is proposed for the elliptic algebra Aq,p(ŝl2).