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arXiv · 1606.01082

Classification of finite irreducible conformal modules over some Lie conformal algebras related to the Virasoro conformal algebra

Henan Wu·Lamei Yuan
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Abstract

In this paper, we classify all finite irreducible conformal modules over a class of Lie conformal algebras $\mathcal{W}(b)$ with $b\in\mathbb{C}$ related to the Virasoro conformal algebra. Explicitly, any finite irreducible conformal module over $\mathcal{W}(b)$ is proved to be isomorphic to $M_{\Delta,\alpha,\beta}$ with $\Delta\neq 0$ or $\beta\neq 0$ if $b=0$, or $M_{\Delta,\alpha}$ with $\Delta\neq 0$ if $b\neq0$. As a byproduct, all finite irreducible conformal modules over the Heisenberg-Virasoro conformal algebra and the Lie conformal algebra of $\mathcal{W}(2,2)$-type are classified. Finally, the same thing is done for the Schr\"odinger-Virasoro conformal algebra.

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Henan Wu, Lamei Yuan. 2016-06-03. Classification of finite irreducible conformal modules over some Lie conformal algebras related to the Virasoro conformal algebra. https://doi.org/10.1063/1.4979619

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