Classification of Superconformal Algebras with Quadratic Non-Linearity

Abstract

A unified treatment of both superconformal and quasisuperconformal algebras with quadratic non-linearity is given. General formulas describing their structure are found by solving the Jacobi identities. A complete classification of quasisuperconformal and Z2× Z2-graded algebras are obtained and in addition to the previously known cases five exceotional quasisuperconformal algebras and a series of Z2× Z2-superconformal algebras containing affine sp2osp(N|2M) are constructed.

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