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Griess algebras and conformal vectors in vertex operator algebras. (English) Zbl 0964.17021

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)].

MSC:

17B69 Vertex operators; vertex operator algebras and related structures
17B68 Virasoro and related algebras

Citations:

Zbl 0789.17002
Full Text: DOI