Abstract:
The role of noninvertible transformations in superstring theories is discussed. A new parametrization of superconformal groups is found, which enable us to construct their ideal extensions, superconformal semigroups. The latter consist of a group containing the standard superconformal transformations and of an ideal. The general abstract structure of superconformal groups is analysed in detail. A classification in terms of indices of nilpotency is presented. The ideal series is constructed, and new generalized “vector” and “tensor”
Green's relations and several quasicharacters are defined. The necessity of similar constructions in other supersymmetric and superquantum models is stressed.
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