Bina, Behzad; Günaydin, Murat Real forms of nonlinear superconformal and quasi-superconformal algebras and their unified realization. (English) Zbl 0934.81015 Nucl. Phys., B 502, No. 3, 713-740 (1997). Summary: We give a complete classification of the real forms of simple nonlinear superconformal algebras (SCA) and quasi-superconformal algebras (QSCA) and present a unified realization of these algebras with simple symmetry groups. This classification is achieved by establishing a correspondence between simple nonlinear QSCA’s and SCA’s and quaternionic and super-quaternionic symmetric spaces of simple Lie groups and Lie supergroups, respectively. The unified realization we present involves a dimension zero scalar field (dilaton), dimension-1 symmetry currents, and dimension-{1}/{2} free bosons for QSCA’s and dimension-{1}/{2} free fermions for SCA’s. 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