Abstract
We study the four-dimensional {\it N}=8 maximal supergravity in the context of Lie superalgebra SU(8/1). All possible successive superalgebraic truncations from four-dimensional {\it N}=8 theory to {\it N}=7, 6, , 1 supergravity theories are systematically realized as sub-superalgebra chains of SU(8/1) by using the Kac-Dynkin weight techniques.
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