Abstract
We study $D=5$ and $D=8$ supergravities in the context of superalgebra. These are analyzed in $\mathrm{SU}(\frac{4}{2})$ superalgebra and its branching patterns in terms of Kac-Dynkin weight techniques. Consistent truncations can be easily realized as subalgebra chains of $\mathrm{SU}(\frac{4}{2})$ superalgebras.
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