Journal of the Mathematical Society of Japan

Some modules over Lie algebras related to the Virasoro algebra

Guobo CHEN, Jianzhi HAN, and Yucai SU

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In this paper, we study restricted modules over a class of $(1/2) \mathbb{Z}$-graded Lie algebras $\mathfrak{g}$ related to the Virasoro algebra. We in fact give the classification of certain irreducible restricted $\mathfrak{g}$-modules in the sense of determining each irreducible restricted module up to an irreducible module over a subalgebra of $\mathfrak{g}$ which contains its positive part. Several characterizations of these irreducible $\mathfrak{g}$-modules are given. By the correspondence between restricted modules over $\mathfrak{g}$ and modules over the vertex algebra associated to $\mathfrak{g}$, we get the classification of certain irreducible modules over vertex algebras associated to these $\mathfrak{g}$.


The second author was supported by NSF of China (grant Nos. 11501417, 11671247). The third author was supported by NSF of China (grant No. 11431010).

Article information

J. Math. Soc. Japan, Advance publication (2019), 12 pages.

Received: 2 May 2018
Revised: 25 August 2018
First available in Project Euclid: 2 July 2019

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Digital Object Identifier

Primary: 17B69: Vertex operators; vertex operator algebras and related structures
Secondary: 17B68: Virasoro and related algebras

irreducible module vertex algebra Virasoro algebra restricted module


CHEN, Guobo; HAN, Jianzhi; SU, Yucai. Some modules over Lie algebras related to the Virasoro algebra. J. Math. Soc. Japan, advance publication, 2 July 2019. doi:10.2969/jmsj/80488048.

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