The Frank Lie algebras are simple Lie algebras that only occur over fields of characteristic 3. These come equipped with distinguished inner derivations that make them algebras in the category $\textbf{ Rep}(\alpha_3)$. We apply the semisimplification functor to these Frank Lie algebras and obtain modular contact Lie superalgebras. We also obtain a class of simple $J$-ternary algebras whose associated Jordan algebras are not simple.
Categories: math.RA