intermediate series
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2021 ◽  
Vol 28 (02) ◽  
pp. 319-336
Author(s):  
Yadi Wu ◽  
Xiaoqing Yue

Let [Formula: see text] be a class of not-finitely graded Lie algebras related to generalized Virasoro algebras with basis [Formula: see text], which satisfies relations [Formula: see text] and [Formula: see text]. In this paper, [Formula: see text]-modules of the intermediate series satisfying some conditions are constructed and classified. We also obtain modules of the intermediate series over the related Lie superalgebra.


2020 ◽  
Vol 27 (02) ◽  
pp. 343-360 ◽  
Author(s):  
Hengyun Yang ◽  
Ying Xu ◽  
Jiancai Sun

The topological N = 2 superconformal algebra was introduced by Dijkgraaf, Verlinde and Verlinde as the symmetry algebra of topological strings at d < 1. We give a classification of irreducible 𝕫 × 𝕫-graded modules of the intermediate series over this infinite-dimensional Lie superalgebra.


Author(s):  
Xiu Han ◽  
Dengyin Wang ◽  
Chunguang Xia

Let [Formula: see text] be a Lie conformal algebra related to Galilean conformal algebras, where [Formula: see text] are complex numbers. All the conformal derivations of [Formula: see text] are shown to be inner. The rank one conformal modules and [Formula: see text]-graded free intermediate series modules over [Formula: see text] are completely classified. The corresponding results of the finite conformal subalgebra of [Formula: see text] are also obtained as byproducts.


2019 ◽  
Vol 26 (03) ◽  
pp. 529-540
Author(s):  
Xiufu Zhang ◽  
Shaobin Tan ◽  
Haifeng Lian

The conjugate-linear anti-involutions and unitary irreducible modules of the intermediate series over the twisted Heisenberg–Virasoro algebra are classified, respectively. We prove that any unitary irreducible module of the intermediate series over the twisted Heisenberg–Virasoro algebra is of the form [Formula: see text] for [Formula: see text], [Formula: see text] and [Formula: see text].


2016 ◽  
Vol 45 (2) ◽  
pp. 749-763 ◽  
Author(s):  
Yan Wang ◽  
Qiaozhi Geng ◽  
Zhiqi Chen
Keyword(s):  

2016 ◽  
Vol 27 (06) ◽  
pp. 1650057 ◽  
Author(s):  
Haibo Chen ◽  
Jianzhi Han ◽  
Yucai Su ◽  
Ying Xu

In this paper, we introduce two kinds of Lie conformal algebras, associated with the loop Schrödinger–Virasoro Lie algebra and the extended loop Schrödinger–Virasoro Lie algebra, respectively. The conformal derivations, the second cohomology groups of these two conformal algebras are completely determined. And nontrivial free conformal modules of rank one and [Formula: see text]-graded free intermediate series modules over these two conformal algebras are also classified in the present paper.


2015 ◽  
Vol 17 (05) ◽  
pp. 1550059
Author(s):  
Yucai Su ◽  
Xiaoqing Yue

Let [Formula: see text] be the Lie algebra of Block type with basis {Li,j | i,j ∈ ℤ} and relations [Li,j, Lk,l] = ((j + 1)k - (l + 1)i)Li+k,j+l. Since [Formula: see text] is ℤ2-graded, it is natural to study ℤ2-graded modules over [Formula: see text]. In this paper, ℤ2-graded [Formula: see text]-modules of the intermediate series are classified.


2015 ◽  
Vol 22 (03) ◽  
pp. 367-382 ◽  
Author(s):  
Ming Gao ◽  
Ying Xu ◽  
Xiaoqing Yue

Let L be a Lie algebra of Block type over ℂ with basis {Lα,i | α,i ∈ ℤ} and brackets [Lα,i,Lβ,j]=(β(i+1)-α(j+1)) Lα+β,i+j. In this paper, we first construct a formal distribution Lie algebra of L. Then we decide its conformal algebra B with ℂ[∂]-basis {Lα(w) | α ∈ ℤ} and λ-brackets [Lα(w)λ Lβ(w)]= (α∂+(α+β)λ) Lα+β(w). Finally, we give a classification of free intermediate series B-modules.


2014 ◽  
Vol 21 (02) ◽  
pp. 295-306 ◽  
Author(s):  
Wei Wang ◽  
Ying Xu ◽  
Taijie You

A classification of indecomposable modules of the intermediate series over the deformative Schrödinger-Virasoro Lie algebras is obtained.


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