N=1 Neveu-Schwarz vertex operator superalgebras over Grassmann algebras and with odd formal variables

Abstract

The notions of N=1 Neveu-Schwarz vertex operator superalgebra over a Grassmann algebra and with odd formal variables and of N=1 Neveu-Schwarz vertex operator superalgebra over a Grassmann algebra and without odd formal variables are introduced, and we show that the respective categories of such objects are isomorphic. The weak supercommutativity and weak associativity properties for an N=1 Neveu-Schwarz vertex operator superalgebra with odd formal variables are established, and we show that in the presence of the other axioms, weak supercommutativity and weak associativity are equivalent to the Jacobi identity. In addition, we prove the supercommutativity and associativity properties for an N=1 Neveu-Schwarz vertex operator superalgebra with odd formal variables and show that in the presence of the other axioms, supercommutativity and associativity are equivalent to the Jacobi identity.

arXiv comment34 pages, LaTeX

References in corpus (1)

• Introduction to vertex operator algebras II

Cited by in corpus (6)

• Twisted modules for N=2 supersymmetric vertex operator superalgebras arising from finite automorphisms of the N=2 Neveu-Schwarz algebra
• On axiomatic aspects of N=2 vertex superalgebras with odd formal variables, and deformations of N=1 vertex superalgebras
• On uniformization of N=2 superconformal and N=1 superanalytic DeWitt super-Riemann surfaces
• Automorphism groups of N=2 superconformal super-Riemann spheres
• The notion of N=1 supergeometric vertex operator superalgebra and the isomorphism theorem
• The moduli space of N=2 super-Riemann spheres with tubes