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Qiu-Fan Chen

Publications and source records attributed to Qiu-Fan Chen.

6 recordsLinked to original sources
arXiv2026

A new class of irreducible modules over the BMS-Kac-Moody algebra

In this paper, we construct a class of non-weight modules over the BMS-Kac-Moody algebra by taking tensor products of finitely many irreducible modules $\Phi(\lambda,\a,\b,\r,h(t))$ with irreducible restricted modules. We obtain the necessary and sufficient conditions for these tensor product modules to be irreducible, and determine the corresponding conditions for two such modules to be isomorphic. Moreover, we compare these modules with other known non-weight modules, showing that these irreducible modules are new.

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arXiv2024

Tensor product weight modules over the affine-Virasoro algebra

In this paper, we study the tensor products of irreducible highest weight modules with irreducible loop modules over the affine-Virasoro algebra with aid of the ``shifting technique" established for the Virasoro algebra in [H. Chen, X. Guo, K. Zhao, Tensor product weight modules over the Virasoro algebra, J. Lond. Math. Soc. 88(2013), 829-844.]. All such tensor product modules are indecomposable modules with infinite-dimensional weight spaces. Moreover, we obtain the necessary and sufficient conditions for such tensor product modules to be irreducible. Therefore, we obtain a class of new irreducible weight modules over the affine-Virasoro algebra. Finally, the necessary and sufficient conditions for any two such tensor product modules to be isomorphic are also determined.

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arXiv2021

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

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 $V(η, ε, θ)$. 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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arXiv2021

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

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 [Q. Chen, J. Han, Non-weight modules over the affine-Virasoro algebra of type $A_1$, J. Math. Phys. 60, 071707 (2019)] 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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arXiv2018

Non-weight modules over algebras related to the Virasoro algebra

In this paper, we study a class of non-weight modules over two kinds of algebras related to the Virasoro algebra, i.e., the loop-Virasoro algebras $\mathfrak{L}$ and a class of Block type Lie algebras $\mathfrak{B(q)}$, where $q$ is a nonzero complex number. We determine those modules whose restriction to the Cartan subalgebra (modulo center) are free of rank one. We also provide a sufficient and necessary condition for such modules to be simple, and determine their isomorphism classes. Moreover, we obtain the simplicity of modules over loop-Virasoro algebras by taking tensor products of some irreducible modules mentioned above with irreducible highest weight modules or Whittaker modules.

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