Verma Modules Over the Generalized Heisenberg–Virasoro Algebra

Abstract

Abstract. For any additive subgroup G of an arbitrary field F of characteristic zero, there corresponds a generalized Heisenberg-Virasoro algebra L [G]. Given a total order of G compatible with its group structure, and any h, h I , c, cis defined. In the this note, the irreducibility of Verma modules M (h, h I , c, c I , c LI ) is completely determined.

Generalized Verma Modules over Lie Algebras of Weyl Type

“…The second main result of this paper is the following (its analog for some other Lie algebras can be found, e.g., in [4,8,18,19]). For convenience, we denote L = W(Γ) and set L α,i = t α [D] i for α ∈ Γ and i ∈ Z + .…”

Verma modules over deformed generalized Heisenberg-Virasoro algebras

“…Replacing Z by an arbitrary additive subgroup G of C, one gets the so-called generalized Heisenberg-Virasoro algebra HV [G]. Structure and representations of HV [G] were studied in [8,10,12]. In particular, the irreducible Harish-Chandra modules over HV [G] were classified in [8].…”

Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras

“…It is the natural generalization of the twisted Heisenberg-Virasoro algebra. The structure and representations for generalized Heisenberg-Virasoro algebra were studied in [5], [9]. However, Lie bialgebra structures on generalized Heisenberg-Virasoro algebra have not yet been considered.…”