Verma Modules over a Block Lie Algebra

Abstract

Abstract. Let B be the Lie algebra with basisIt is proved that an irreducible highest weight B-module is quasifinite if and only if it is a proper quotient of a Verma module. For an additive subgroup Γ of F, there corresponds to a Lie algebra B(Γ) of Block type. Given a total order ≻ on Γ and a weight Λ, a Verma B(Γ)-module M (Λ, ≻) is defined. The irreducibility of M (Λ, ≻) is completely determined.

Representations of Generalized Loop Planar Galilean Conformal Algebras W(Γ)

“…[H k+1,s , L −u,i H −λ,j I −v,ε J −l,q ]w. (11) By using Lemma 6(1) to the first term on the right hand side of (11), and using Lemma 6( 2) and (3) to the second and third term, respectively, we have…”

“…Recently, some researchers have investigated the Harish-Chandra modules of many important Lie algebras and Lie super algebras [7][8][9], such as twisted Heisenberg-Virasoro algebra [8], Schrödinger-Virasoro algebra [9] and deformative twisted Schrödinger-Virasoro Lie algebra [9]. In references [10][11][12][13][14][15][16][17], the Verma modules of some Lie algebras and super algebras have been determined. The Verma modules of generalized Virasoro algebras were determined in reference [18].…”