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The group of symmetries of the shorter Moonshine module. (English) Zbl 1210.17033

In his PhD Thesis [G. Höhn, Selbstduale Vertexoperatorsuperalgebren und das Babymonster. Bonn. Math. Schr. 286. Bonn: Univ. Bonn, Mathematisch-Naturwissenschaftliche Fakultät (Diss. 1995) (1996; Zbl 0997.17500)] the author constructed a vertex operator superalgebra, known as the shorter Moonshine module. It is a vertex operator superalgebra of central charge \(23\frac{1}{2}\) on which the direct product of a cyclic group of order two and Fisher’s Baby Monster group acts by automorphisms. In the note under review the author proves that this direct product is, in fact, the whole automorphism group. This was conjectured in the above-mentioned thesis.

MSC:

17B69 Vertex operators; vertex operator algebras and related structures
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
20D08 Simple groups: sporadic groups

Citations:

Zbl 0997.17500
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References:

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