Mathematics – Representation Theory
Scientific paper
2008-11-09
Mathematics
Representation Theory
14 pages; contribution to proceedings of the conference "Moonshine - The First Quarter Century and Beyond"
Scientific paper
In the 1980's, the work of Frenkel, Lepowsky and Meurman, along with that of Borcherds, culminated in the notion of vertex operator algebra, and an example whose full symmetry group is the largest sporadic simple group: the Monster. Thus it was shown that the vertex operators of mathematical physics play a role in finite group theory. In this article we describe an extension of this phenomenon by introducing the notion of enhanced vertex operator algebra, and constructing examples that realize other sporadic simple groups, including one that is not involved in the Monster.
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