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

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 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

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

scholarly journals Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras

2012 ◽  
Vol 55 (3) ◽  
pp. 697-709 ◽  
Author(s):  
Xiangqian Guo ◽  
Rencai Lu ◽  
Kaiming Zhao
Keyword(s):  
Direct Summand ◽  
Virasoro Algebra ◽  
Additive Subgroup ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Intermediate Series ◽  
Complex Number Field ◽  
Weight Modules

AbstractLet G be an arbitrary non-zero additive subgroup of the complex number field ℂ, and let Vir[G] be the corresponding generalized Virasoro algebra over ℂ. In this paper we determine all irreducible weight modules with finite-dimensional weight spaces over Vir[G]. The classification strongly depends on the index group G. If G does not have a direct summand isomorphic to ℤ (the integers), then such irreducible modules over Vir[G] are only modules of intermediate series whose weight spaces are all one dimensional. Otherwise, there is one further class of modules that are constructed by using intermediate series modules over a generalized Virasoro subalgebra Vir[G0] of Vir[G] for a direct summand G0 of G with G = G0 ⊕ ℤb, where b ∈ G \ G0. This class of irreducible weight modules do not have corresponding weight modules for the classical Virasoro algebra.

Modules over algebras related to the Virasoro algebra

2015 ◽  
Vol 26 (09) ◽  
pp. 1550070 ◽  
Author(s):  
Qiufan Chen ◽  
Yan-an Cai
Keyword(s):  
Lie Algebras ◽  
Cartan Subalgebra ◽  
Virasoro Algebra ◽  
Schrödinger Algebra ◽  
Weight Modules

In this paper, we consider a class of non-weight modules for some algebras related to the Virasoro algebra: The algebra Vir (a, b), the twisted deformative Schrödinger–Virasoro Lie algebras and the Schrödinger algebra. We study the modules whose restriction to the Cartan subalgebra (modulo center) are free of rank 1 for these algebras. Moreover, the simplicities of these modules are determined.

scholarly journals Representations of the Twisted Heisenberg–Virasoro Algebra at Level Zero

2003 ◽  
Vol 46 (4) ◽  
pp. 529-537 ◽  
Author(s):  
Yuly Billig
Keyword(s):  
Lie Algebra ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Highest Weight ◽  
Level Zero ◽  
Maximal Submodule ◽  
Highest Weight Modules ◽  
Weight Modules

AbstractWe describe the structure of the irreducible highest weight modules for the twisted Heisenberg–Virasoro Lie algebra at level zero. We prove that either a Verma module is irreducible or its maximal submodule is cyclic.

scholarly journals Non-weight modules over the Heisenberg–Virasoro algebra and the W algebra W(2,2)

2017 ◽  
Vol 16 (05) ◽  
pp. 1750097 ◽  
Author(s):  
Hongjia Chen ◽  
Xiangqian Guo
Keyword(s):  
Cartan Subalgebra ◽  
Virasoro Algebra ◽  
Interesting Case ◽  
Universal Enveloping Algebra ◽  
Simple Modules ◽  
Enveloping Algebra ◽  
Weight Modules

In this paper, we construct and study some non-weight modules for the Heisenberg–Virasoro algebra and the [Formula: see text] algebra [Formula: see text]. We determine the modules, whose restriction to the universal enveloping algebra of the degree-[Formula: see text] part (modulo center) are free of rank [Formula: see text] for these two algebras. In the most interesting case, this degree-[Formula: see text] part is not the Cartan subalgebra. We also determine the simplicity of these modules, which provide new simple modules for the [Formula: see text] algebra [Formula: see text].

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