Twisted Γ-Lie algebras and their vertex operator representations

Let Gamma be a generic subgroup of the multiplicative group C* of nonzero complex numbers. We define a class of Lie algebras associated to Gamma, called twisted P-Lie algebras, which are natural generalizations of the twisted affine Lie algebras. Starting from an arbitrary even sublattice Q of Z(N) and an arbitrary finite order isometry of ZN preserving Q, we construct a family of twisted P-vertex operators acting on generalized Fock spaces which afford irreducible representations for certain twisted F-Lie algebras. As an application, this recovers a number of known vertex operator realizations for infinite dimensional Lie algebras, such as twisted affine Lie algebras, extended affine Lie algebras of type A, trigonometric Lie algebras of series A and B, unitary Lie algebras, and BC-graded Lie algebras. (C) 2014 Elsevier Inc. All rights reserved.