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Simple currents and extensions of vertex operator algebras. (English) Zbl 0873.17027

The authors give a construction of extending a vertex operator algebra to an abelian intertwining algebra by certain “simple currents”. These simple currents are variations of the vertex operator algebra by a weight-one primary vector. Moreover, the rationality of the extended algebra is discussed when it forms a vertex operator algebra. Furthermore, they apply their construction to affine Kac-Moody algebras.

MSC:

17B69 Vertex operators; vertex operator algebras and related structures
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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