The Heisenberg-Virasoro Lie conformal superalgebra

Haibo Chen; Xiansheng Dai; Yanyong Hong

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arXiv · 2009.06853

The Heisenberg-Virasoro Lie conformal superalgebra

Haibo Chen·Xiansheng Dai·Yanyong Hong

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Abstract

In this paper, we introduce a finite Lie conformal superalgebra called the Heisenberg-Virasoro Lie conformal superalgebra $\mathfrak{s}$ by using a class of Heisenberg-Virasoro Lie conformal modules. The super Heisenberg-Virasoro algebra of Ramond type $§$ is defined by the formal distribution Lie superalgebra of $\mathfrak{s}$. Then we construct a class of simple $§$-modules, which are induced from simple modules of some finite dimensional solvable Lie superalgebras. These modules are isomorphic to simple restricted $§$-modules, and include the highest weight modules, Whittaker modules and high order Whittaker modules. As a byproduct, we present a subalgebra of $§$, which is isomorphic to the super Heisenberg-Virasoro algebra of Neveu-Schwarz type.

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BibTeX RIS

Haibo Chen, Xiansheng Dai, Yanyong Hong. 2023-05-29. The Heisenberg-Virasoro Lie conformal superalgebra. https://arxiv.org/abs/2009.06853

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