# zbMATH — the first resource for mathematics

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
Full Text: