On the unitary structures of vertex operator superalgebras

In this paper, the notion of unitary vertex operator super algebra is introduced. It is proved that vertex operator super-algebras associated to unitary highest weight representations for the Neveu-Schwarz Lie superalgebra, Heisenberg superalgebras and to positive definite integral lattices are unitary vertex operator superalgebras. The unitary structures are then used to study the structures of vertex operator superalgebras, it is proved that any unitary vertex operator superalgebra is a direct sum of strong OFT type unitary simple vertex operator superalgebras. The classification of unitary vertex operator superalgebras generated by subspaces with conformal weights less than or equal to 1 is also considered. (C) 2017 Elsevier Inc. All rights reserved.