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Journal Article

#### Vertex operator algebras, minimal models, and modular linear differential equations of order 4

##### External Ressource

https://doi.org/10.2969/jmsj/74957495

(Publisher version)

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##### Citation

Arike, Y., Nagatomo, K., & Sakai, Y. (2018). Vertex operator algebras, minimal
models, and modular linear differential equations of order 4.* Journal of the Mathematical Society
of Japan,* *70*(4), 1347-1373. doi:10.2969/jmsj/74957495.

Cite as: http://hdl.handle.net/21.11116/0000-0003-C4EB-7

##### Abstract

In this paper we classify vertex operator algebras with three conditions which arise from Virasoro minimal models: (A) the central charge and conformal weights are rational numbers, (B) the space spanned by characters of all simple modules of a vertex operator algebra coincides with the space of solutions of a modular linear differential equation of order 4 and (C) the dimensions of first three weight subspaces of a VOA are 1, 0 and 1, respectively. It is shown that vertex operator algebras which we concern have central charges c= −46/3, −3/5, −114/7, 4/5, and are isomorphic to minimal models for c= −46/3, −3/5 and $Z_2$
-graded simple current extensions of minimal models for c= −114/7, 4/5.