Classification of indecomposable modules of the intermediate series over the twisted N=2 superconformal algebra

Li, Junbo; Su, Yucai; Zhu, Linsheng

doi:10.1063/1.3460855

Cited by 17 publications

(6 citation statements)

References 29 publications

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“…In the following, we define the weighting functor W for L by taking h = t = CL 0 . The weight modules called intermediate series of the twisted N = 2 superconformal algebra were investigated in [12]. The following theorem obtained by a very natural extension of [12].…”

Section: Intermediate Series Modulesmentioning

confidence: 99%

“…Some characteristics related to the structure of Verma modules over the twisted N = 2 superconformal algebra were investigated in [6,9]. The classification of indecomposable modules of the intermediate series over the twisted N = 2 superconformal algebra was achieved in [12]. All simple Harish-Chandra modules over the N = 1 and untwisted N = 2 superconformal algebras were classified respectively in [11,16].…”

Section: Introductionmentioning

confidence: 99%

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A family of simple non-weight modules over the twisted $N=2$ superconformal algebra

Chen¹,

Dai²,

Liu³

2021

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We construct a class of non-weight modules over the twisted N = 2 superconformal algebra L. Let h = CL 0 ⊕ CG 0 be the Cartan subalgebra of L, and let t = CL 0 be the Cartan subalgebra of even part L0. These modules over L when restricted to the h are free of rank 1 or when restricted to the t are free of rank 2. We provide the sufficient and necessary conditions for those modules being simple, as well as giving the sufficient and necessary conditions for two L-modules being isomorphic. We also compute the action of an automorphism on them. Moreover, based on the weighting functor introduced in [15], a class of intermediate series modules A t (σ) are obtained. As a byproduct, we give a sufficient condition for two L-modules are not isomorphic.

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Section: Intermediate Series Modulesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A family of simple non-weight modules over the twisted $N=2$ superconformal algebra

Chen¹,

Dai²,

Liu³

2021

Preprint

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“…Moreover, some special weight modules over the superconformal algebras of N = 1, 2 have been extensively investigated (see, e.g. [7,10,11,12,14,22,9,18,26]). Recently, some families of non-weight modules over the superconformal algebras of N = 1, 2 were studied.…”

Section: Introductionmentioning

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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“…It is known that representations of the superconformal algebras get more and more complicated with increasing the number of fermionic currents N. The classification of all simple Harish-Chandra modules over the N = 1 and untwisted N = 2 superconformal algebras was achieved respectively in [21,16]. Moreover, some special weight modules over the N = 2 superconformal algebras were studied (see [8,11,14,19,25]).…”

Section: Introductionmentioning

confidence: 99%

On non-weight representations of the $N=2$ superconformal algebras

Yang

Yao

Xia

2019

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Classification of indecomposable modules of the intermediate series over the twisted N=2 superconformal algebra

Abstract: In this paper, we classify all simple weight modules with finite dimensional weight spaces over the N = 2 superconformal algebra. (2000): 17B10, 17B65, 17B68, 17B70. Mathematics Subject ClassificationSetting m = 0 in (4.10) we get c − = c − 1.Case 1. c = 0.

Cited by 17 publications

References 29 publications

A family of simple non-weight modules over the twisted $N=2$ superconformal algebra

A family of simple non-weight modules over the twisted $N=2$ superconformal algebra

From super Weyl modules to the super Virasoro modules

On non-weight representations of the $N=2$ superconformal algebras

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