scholarly journals Subsingular vectors in Verma modules, and tensor product of weight modules over the twisted Heisenberg-Virasoro algebra andW(2, 2) algebra

2013 ◽  
Vol 54 (7) ◽  
pp. 071701 ◽  
Author(s):  
Gordan Radobolja
Keyword(s):  
Tensor Product ◽  
Virasoro Algebra ◽  
Verma Modules ◽  
Weight Modules

A Family of Non-weight Modules over the Virasoro Algebra

2020 ◽  
Vol 27 (04) ◽  
pp. 807-820
Author(s):  
Guobo Chen
Keyword(s):  
Tensor Product ◽  
Sufficient Conditions ◽  
Virasoro Algebra ◽  
Necessary And Sufficient Conditions ◽  
Weight Module ◽  
Highest Weight Module ◽  
Isomorphism Classes ◽  
Highest Weight ◽  
Necessary And Sufficient ◽  
Weight Modules

In this paper, we consider the tensor product modules of a class of non-weight modules and highest weight modules over the Virasoro algebra. We determine the necessary and sufficient conditions for such modules to be simple and the isomorphism classes among all these modules. Finally, we prove that these simple non-weight modules are new if the highest weight module over the Virasoro algebra is non-trivial.

scholarly journals Tensor product weight modules over the Virasoro algebra

2013 ◽  
Vol 88 (3) ◽  
pp. 829-844 ◽  
Author(s):  
Hongjia Chen ◽  
Xiangqian Guo ◽  
Kaiming Zhao
Keyword(s):  
Tensor Product ◽  
Virasoro Algebra ◽  
Product Weight ◽  
Weight Modules

Automorphisms and Verma Modules for Generalized 2-dim Affine-Virasoro Algebra

2017 ◽  
Vol 24 (02) ◽  
pp. 285-296 ◽  
Author(s):  
Wenlan Ruan ◽  
Honglian Zhang ◽  
Jiancai Sun
Keyword(s):  
Automorphism Group ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Verma Modules

We study the structure of the generalized 2-dim affine-Virasoro algebra, and describe its automorphism group. Furthermore, we also determine the irreducibility of a Verma module over the generalized 2-dim affine-Virasoro algebra.

scholarly journals Verma modules over Virasoro-like algebras

2006 ◽  
Vol 80 (2) ◽  
pp. 179-191 ◽  
Author(s):  
Xian-Dong Wang ◽  
Kaiming Zhao
Keyword(s):  
Additive Group ◽  
Total Order ◽  
Verma Modules ◽  
Direct Sum ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules

AbstractLet K be a field of characteristic 0, G the direct sum of two copies of the additive group of integers. For a total order ≺ on G, which is compatible with the addition, and for any ċ1, ċ2 ∈ K, we define G-graded highest weight modules M(ċ1, ċ2, ≺) over the Virasoro-like algebra , indexed by G. It is natural to call them Verma modules. In the present paper, the irreducibility of M (ċ1, ċ2, ≺) is completely determined and the structure of reducible module M (ċ1, ċ2, ≺)is also described.

scholarly journals Non-weight modules over the affine-Virasoro algebra of type A1

2019 ◽  
Vol 60 (7) ◽  
pp. 071707
Author(s):  
Qiufan Chen ◽  
Jianzhi Han
Keyword(s):  
Virasoro Algebra ◽  
Weight Modules

AN EXPLICIT FORMULA FOR SOME SINGULAR VECTORS OF THE NEVEU–SCHWARZ ALGEBRA

1992 ◽  
Vol 07 (13) ◽  
pp. 3023-3033 ◽  
Author(s):  
LOUIS BENOIT ◽  
YVAN SAINT-AUBIN
Keyword(s):  
Explicit Expression ◽  
Explicit Formula ◽  
Singular Vector ◽  
Central Charge ◽  
Discrete Series ◽  
Virasoro Algebra ◽  
Verma Modules ◽  
Singular Vectors ◽  
Highest Weight ◽  
Highest Weight Representations

Similarly to the Virasoro algebra, the Neveu–Schwarz algebra has a discrete series of unitary irreducible highest weight representations. These are labeled by the values of [Formula: see text] (the central charge) and of the highest weight hpq = [(p (m + 2) − qm)2 − 4]/(8m (m + 2)) where m, p, q are some integers. The Verma modules constructed with these values (c, h) are not irreducible, however, as they contain two Verma submodules, each generated by a singular vector ψp,q (of weight hpq + pq/2) and ψm−p, m+2−q (of weight hpq + (m−p)(m+2−q)/2), respectively. We give an explicit expression for these singular vectors whenever one of its indices is 1.

scholarly journals Two classes of non-weight modules over the twisted Heisenberg–Virasoro algebra

2018 ◽  
Vol 160 (1-2) ◽  
pp. 265-284 ◽  
Author(s):  
Haibo Chen ◽  
Jianzhi Han ◽  
Yucai Su ◽  
Xiaoqing Yue
Keyword(s):  
Virasoro Algebra ◽  
Weight Modules

A class of simple non-weight modules over the virasoro algebra

2020 ◽  
Vol 63 (4) ◽  
pp. 956-970 ◽  
Author(s):  
Haibo Chen ◽  
JianZhi Han
Keyword(s):  
Tensor Product ◽  
Sufficient Conditions ◽  
Virasoro Algebra ◽  
Vector Spaces ◽  
Complex Numbers ◽  
Infinite Dimensional ◽  
Highest Weight ◽  
Alpha Omega ◽  
Necessary And Sufficient ◽  
Infinite Dimensional Lie Algebra

AbstractThe Virasoro algebra $\mathcal {L}$ is an infinite-dimensional Lie algebra with basis {Lm, C| m ∈ ℤ} and relations [Lm, Ln] = (n − m)Lm+n + δm+n,0((m3 − m)/12)C, [Lm, C] = 0 for m, n ∈ ℤ. Let $\mathfrak a$ be the subalgebra of $\mathcal {L}$ spanned by Li for i ≥ −1. For any triple (μ, λ, α) of complex numbers with μ ≠ 0, λ ≠ 0 and any non-trivial $\mathfrak a$-module V satisfying the condition: for any v ∈ V there exists a non-negative integer m such that Liv = 0 for all i ≥ m, non-weight $\mathcal {L}$-modules on the linear tensor product of V and ℂ[∂], denoted by $\mathcal {M}(V,\mu ,\Omega (\lambda ,\alpha ))\ (\Omega (\lambda ,\alpha )=\mathbb {C}[\partial ]$ as vector spaces), are constructed in this paper. We prove that $\mathcal {M}(V,\mu ,\Omega (\lambda ,\alpha ))$ is simple if and only if μ ≠ 1, λ ≠ 0, α ≠ 0. We also give necessary and sufficient conditions for two such simple $\mathcal {L}$-modules being isomorphic. Finally, these simple $\mathcal {L}$-modules $\mathcal {M}(V,\mu ,\Omega (\lambda ,\alpha ))$ are proved to be new for V not being the highest weight $\mathfrak a$-module whose highest weight is non-zero.

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