2016
DOI: 10.1063/1.4965877
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A class of simple weight modules over the twisted Heisenberg-Virasoro algebra

Abstract: A class of weight modules M(V,a) over the twisted Heisenberg-Virasoro H are constructed, which includes modules of intermediate series, where V is an H̄r,d-module and a is a complex number. We give the necessary and sufficient conditions under which these modules are simple and also determine all the equivalent simple modules in this class. Moreover, we show that simple modules in this class are new. Finally, we construct a class of new simple non-weight H-modules.

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Cited by 6 publications
(14 citation statements)
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“…carries the structure of an L-module under the above given actions, which is denoted by M(V, γ(t)). Note from [9] that M(V, γ(t)) is a weight L-module if and only if γ(t) ∈ C and also that the L-module M(V, γ(t)) for γ(t) ∈ C[t, t −1 ] is simple if and only if V is simple (see also [2]). Proposition 5.1.…”
Section: Isomorphism Classesmentioning
confidence: 99%
“…carries the structure of an L-module under the above given actions, which is denoted by M(V, γ(t)). Note from [9] that M(V, γ(t)) is a weight L-module if and only if γ(t) ∈ C and also that the L-module M(V, γ(t)) for γ(t) ∈ C[t, t −1 ] is simple if and only if V is simple (see also [2]). Proposition 5.1.…”
Section: Isomorphism Classesmentioning
confidence: 99%
“…And irreducible Harish-Chandra H-modules were classified in [15], each of which was shown to be either the highest (or lowest) weight module, or the module of intermediate series, consistent with the well-known result for Virasoro algebra [16]. While weight modules with an infinite dimensional weight subspace were also studied (see [6,19]). Non-weight modules constitute the other important ingredients of the representation theory of H, the study of which is definitely necessary and became popular in the last few years.…”
mentioning
confidence: 67%
“…sending w ⊗ v n to i ( λ 2 λ 1 ) n n i u i ⊗ v n for any n ∈ Z by Lemma 4.2 and Proposition 4.3 , and on the other hand that φ A (w ⊗ v n ) = ϕ(w) ⊗ v n for any n ∈ Z (see [6,Theorem 4.1]). Thus,…”
Section: Isomorphism Classesmentioning
confidence: 99%
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