The Conway-Miyamoto correspondences for the Fischer 3-transposition groups

Lam, Ching Hung; Yamauchi, Hiroshi

doi:10.1090/tran/8589

The Conway-Miyamoto correspondences for the Fischer 3-transposition groups
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Trans. Amer. Math. Soc. 375 (2022), 2025-2067 Request permission

Abstract:

In this paper, we present a general construction of 3-transposition groups as automorphism groups of vertex operator algebras. Applying to the moonshine vertex operator algebra, we establish the Conway-Miyamoto correspondences between Fischer 3-transposition groups $\mathrm {Fi}_{23}$ and $\mathrm {Fi}_{22}$ and $c=25/28$ and $c=11/12$ Virasoro vectors of subalgebras of the moonshine vertex operator algebra.

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