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Han, Jianzhi; Chen, Qiufan; Su, Yucai

doi:10.1016/j.laa.2016.11.002

Cited by 33 publications

(16 citation statements)

References 8 publications

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“…In recent years, many authors constructed various irreducible non-Harish-Chandra modules and irreducible non-weight modules (cf. [1], [3,4], [12], [19]- [24]). In particular, J.…”

Section: It Is Well Known That Representation Theory Of the Virasoro ...mentioning

confidence: 99%

Irreducible tensor product modules over the affine-Virasoro algebra of type $A_1$

Chen¹,

Yao²

2021

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In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type A 1 by taking tensor products of irreducibles defined in [7] with irreducible highest weight modules. The irreducibility and the isomorphism classes of these modules are determined. Moreover, we show that these tensor product modules are different from the known non-weight modules. Finally, we realize some tensor product modules as induced modules from modules over certain subalgebras of the affine-Virasoro algebra of type A 1 , and give sufficient and necessary conditions for these induced modules to be reducible.

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“…In recent years, many authors constructed various irreducible non-Harish-Chandra modules and irreducible non-weight modules (cf. [1], [3,4], [12], [19]- [24]). In particular, J.…”

Section: It Is Well Known That Representation Theory Of the Virasoro ...mentioning

confidence: 99%

Irreducible tensor product modules over the affine-Virasoro algebra of type $A_1$

Chen¹,

Yao²

2021

Preprint

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“…In [18], Tan and Zhao obtained them by a very different method. From then on, the free U(h)-modules were widely investigated over all kinds of Lie algebras, such as the finite-dimensional simple Lie algebras [15] and the infinite-dimensional Lie algebras related to Virasoro algebras and so on (see, e.g., [2,4,8,13,17,19,20]). It is worth mentioning that the free U(h)-modules over some Lie superalgebras were also characterized.…”

Section: Introductionmentioning

confidence: 99%

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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“…In recent years, many authors constructed various irreducible non-Harish-Chandra modules and irreducible non-weight modules (cf. [1], [3,4], [15], [23]- [29]). In particular, J.…”

Section: Introductionmentioning

confidence: 99%

A new class of irreducible modules over the affine-Virasoro algebra of type $A_1$

Chen¹,

Yao²

2021

Preprint

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In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type A 1 by taking tensor products of a finite number of irreducible modules M (λ, α, β, γ) with irreducible highest weight modules V (η, ǫ, θ). We obtain the necessary and sufficient conditions for such tensor product modules to be irreducible, and determine the necessary and sufficient conditions for such two modules to be isomorphic.We also compare these modules with other known non-weight modules, showing that these irreducible modules are new.

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Modules over the algebra Vir(a,b)

Cited by 33 publications

References 8 publications

Irreducible tensor product modules over the affine-Virasoro algebra of type $A_1$

Irreducible tensor product modules over the affine-Virasoro algebra of type $A_1$

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

A new class of irreducible modules over the affine-Virasoro algebra of type $A_1$

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