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Vertex operator superalgebras and their representations. (English) Zbl 0838.17035
Sally, Paul J. jun. (ed.) et al., Mathematical aspects of conformal and topological field theories and quantum groups. AMS-IMS-SIAM summer research conference, June 13-19, 1992, Mount Holyoke College, South Hadley, MA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 175, 161-191 (1994).
I. B. Frenkel and Y. Zhu [Duke Math. J. 66, 123-168 (1992)] associated to any vertex operator algebra (VOA) \(V\) an associative algebra \(A(V)\), and to any \(V\)-module \(M\) an \(A(V)\)-module \(A(M)\). This paper generalizes these constructions to super VOAs. Examples considered include the \(N=1\) super VOAs associated to representations of an affine Lie superalgebra, and to those of the Neveu-Schwarz algebra. The rationality and fusion rules of these super VOAs are discussed.
For the entire collection see [Zbl 0801.00049].

MSC:
17B69 Vertex operators; vertex operator algebras and related structures
17A70 Superalgebras
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
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