## Journal of the Mathematical Society of Japan

### Some modules over Lie algebras related to the Virasoro algebra

#### Abstract

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 $\mathfrak{g}$.

#### Note

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

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

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

https://projecteuclid.org/euclid.jmsj/1562033193

Digital Object Identifier
doi:10.2969/jmsj/80488048

#### Citation

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. https://projecteuclid.org/euclid.jmsj/1562033193

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