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• W1816809675 abstract "The notion of N = 2 vertex superalgebra with two odd formal is presented, the main axiom being a Jacobi identity with odd formal variables in which an N=2 superconformal shift is incorporated into the usual Jacobi identity for a vertex superalgebra. It is shown that as a consequence of these axioms, the N=2 vertex superalgebra is naturally a representation of the Lie algebra isomorphic to the three-dimensional algebra of superderivations with basis consisting of the usual conformal operator and the two N=2 superconformal operators. The notion of N=2 Neveu-Schwarz vertex operator superalgebra with two odd formal variables is introduced, and consequences of this notion are derived. Various other formulations of the notion of N=2 (Neveu-Schwarz) vertex (operator) superalgebra appearing in the mathematics and physics literature are discussed, and several mistakes in the literature are noted and corrected. The notion of ``N=2 (Neveu-Schwarz) vertex (operator) superalgebra with one odd formal variable is formulated. It is shown that this formulation naturally arises from alternate notions of N=1 superconformality and the continuous deformation of an N=1 (Neveu-Schwarz) vertex (operator) superalgebra with one odd formal variable. This notion is formulated to reflect the underlying N=1 superanalytic geometry, and it is shown that the equivalence of the notions of N=2 (Neveu-Schwarz) vertex (operator) superalgebra with one and with two odd formal variables reflects the equivalence of N=2 superconformal and N=1 superanalytic geometry. In particular we prove that the group of formal N=2 superconformal functions vanishing at zero and invertible in a neighborhood of zero is isomorphic to a certain subgroup of N=1 superanalytic functions vanishing at zero and invertible in a neighborhood of zero." @default.
• W1816809675 created "2016-06-24" @default.
• W1816809675 creator A5034296934 @default.
• W1816809675 date "2007-10-30" @default.
• W1816809675 modified "2023-09-27" @default.
• W1816809675 title "On axiomatic aspects of N=2 vertex superalgebras with odd formal variables, and deformations of N=1 vertex superalgebras" @default.
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• W1816809675 hasPublicationYear "2007" @default.
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