Miyamoto, Masahiko Griess algebras and conformal vectors in vertex operator algebras. (English) Zbl 0964.17021 J. Algebra 179, No. 2, 523-548 (1996). Summary: We define automorphisms of vertex operator algebra using the representations of the Virasoro algebra. In particular, we show that the existence of a special element, which we will call a “rational conformal vector with central charge \(\frac 12\),” implies the existence of an automorphism of a vertex operator algebra. This result offers a simple construction of triality involutions of the Moonshine module \(V^\#\). We also study the structures of Griess algebras and prove a conjecture given by Meyer and Neutsch that the maximal dimension of associative subalgebras of the Griess Monster algebra is 48 [ see W. Meyer and W. Neutsch, J. Algebra 158, 1-17 (1993; Zbl 0789.17002)]. Cited in 9 ReviewsCited in 89 Documents MSC: 17B69 Vertex operators; vertex operator algebras and related structures 17B68 Virasoro and related algebras Keywords:automorphisms; vertex operator algebra; Griess algebras; Virasoro algebra; Moonshine module Citations:Zbl 0789.17002 × Cite Format Result Cite Review PDF Full Text: DOI