Irreducible representations of Virasoro-toroidal Lie algebras

Toroidal Lie algebras and their vertex operator representations were introduced by R. V. Moody, R. S. Eswara, and T. Yokonuma (1990) and a class of indecomposable modules were investigated. In this work, we extend the toroidal algebra by the Virasoro algebra thus constructing a semi-direct product algebra containing the toroidal algebra as an ideal and the Virasoro algebra as a subalgebra. With the use of vertex operators and certain oscillator representations of the Virasoro algebra it is proved that the corresponding Fock space gives rise to a class of irreducible modules for the Virasoro-toroidal algebra. (orig.)