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 Z 2 × Z 2-graded algebras is obtained and in addition to the previously known cases five exceptional quasisuperconformal algebras and a series of Z 2 × Z 2-superconformal algebras containing affine sp 2⊕ osp (N|2M) are constructed.
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