Automorphisms and Verma modules for generalized Schrödinger–Virasoro algebras

Let F be a field of characteristic 0, G an additive subgroup of F, α∈F satisfying α∉G and 2α∈G. We define a class of infinite-dimensional Lie algebras which are called generalized Schrödinger–Virasoro algebras and denoted by gsv[G,α]. In this paper the automorphism group and irreducibility of Verma modules for gsv[G,α] are completely determined.