Abstract
A list of superconformal chiral operator product expansion algebras with quadratic nonlinearity in two dimensions is completed on the basis of the known classification of little conformal Lie superalgebras. In addition to the previously known cases and the in our previous paper constructed exceptional N=8 superalgebra associated with F(4), a novel exceptional N=7 superconformal algebra associated with G(3) is found, as well as a whole family of superalgebras containing affine su 2⊕ usp 2N . A classification scheme for quasisuperconformal algebras is also outlined.
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