Automorphisms and Verma modules for Generalized Schrödinger-Virasoro algebras

Abstract

Let $\mathbb{F}$ be a field of characteristic 0, $G$ an additive subgroup of $\mathbb{F}$, $\alpha \in \mathbb{F}$ satisfying $\alpha \notin G,2\alpha \in G$. We define a class of infinite-dimensional Lie algebras which are called generalized Schrödinger-Virasoro algebras and use $\mathfrak{gsv}[G,\alpha ]$ to denote the one corresponding to $G$ and $\alpha$. In this paper the automorphism group and irreducibility of Verma modules for $\mathfrak{gsv}[G,\alpha ]$ are completely determined.

18 pages

References in corpus (1)

• Structure of the extended Schrodinger-Virasoro Lie algebra