Irreducible Twisted Heisenberg–Virasoro Modules from Tensor Products

Chen, Haibo; Su, Yucai

doi:10.1007/s00025-019-1109-5

Cited by 5 publications

(2 citation statements)

References 38 publications

(74 reference statements)

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“…We always suppose that the action of ξ on S-modules A is nontrivial. If not, the R-module M A,b and T -module V A,b will be respectively reduced to the Virasoro module (see [20]) and the twisted Heisenberg-Virasoro module (see [20,6]).…”

Section: 2mentioning

confidence: 99%

From super Weyl modules to the super Virasoro modules

Chen¹,

Dai²,

Liu³

2021

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Based on the classification of irreducible modules over the Weyl superalgebra S, the restriction functor and the "twisting technique", we construct a class of new (generally non-weight) modules over the N = 1, 2 Ramond algebras R and T . The sufficient and necessary conditions for these modules to be irreducible are determined. In addition, lots of interesting examples for such irreducible modules over the N = 1, 2 Ramond algebras with different features are given, which include super intermediate series modules, U(CL 0 )-free modules of rank two, super degree two modules and so on. Finally, we obtain that some of these non-weight modules over the N = 1, 2 Ramond algebras are both new. Note that the Witt superalgebra, the N = 2 Neveu-Schwarz algebra and the N = 2 topological algebra are isomorphic to T by spectral flows. As a byproduct, we also give a characterization of the irreducibility of goal modules over these Lie superalgebras (namely, untwisted N = 2 superconformal algebras).

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Section: 2mentioning

confidence: 99%

From super Weyl modules to the super Virasoro modules

Chen¹,

Dai²,

Liu³

2021

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“…the Virasoro algebra [11,14], the Heisenberg-Virasoro algebra [4,5], the algebra V ir(a, b) [9]. Another interesting thing is that this kind of non-weight modules are considered on Lie superalgebras.…”

Section: Introductionmentioning

confidence: 99%

Non-weight modules over the super-BMS$_3$ algebra

Chen¹,

Dai²,

Liu³

et al. 2019

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In the present paper, a class of non-weight modules over the super-BMS 3 algebras S ǫ (ǫ = 0 or 1 2 ) are constructed. These modules when regarded as S 0 -modules and further restricted as modules over the Cartan subalgebra h are free of rank 1, while when regarded as S 1 2 -modules and further restricted as modules over the Cartan subalgebra H are free of rank 2. We determine the necessary and sufficient conditions for these modules being simple, as well as determining the necessary and sufficient conditions for two S ǫ -modules being isomorphic. At last, we present that these modules constitute a complete classification of free U (h)-modules of rank 1 over S 0 , and also constitute a complete classification of free U (H)-modules of rank 2 over S 1 2 .

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U ( h ) -free modules over the super-Galilean conformal algebras

Xie

Sun

Yang

2022

Journal of Mathematical Physics

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In this paper, we study non-weight modules over the super-Galilean conformal algebra. We construct and classify [Formula: see text]-free modules of rank 1 over the Ramond-type algebra and [Formula: see text]-free modules of rank 2 over the Neveu–Schwarz-type algebra, where [Formula: see text] is a subalgebra of the Ramond-type algebra and [Formula: see text] is the Cartan algebra of the Neveu–Schwarz-type algebra. We find that these modules are reducible and isomorphic.

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Irreducible Twisted Heisenberg–Virasoro Modules from Tensor Products

Cited by 5 publications

References 38 publications

From super Weyl modules to the super Virasoro modules

From super Weyl modules to the super Virasoro modules

Non-weight modules over the super-BMS$_3$ algebra

U ( h ) -free modules over the super-Galilean conformal algebras

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