Every Lie superalgebra $\mathfrak{g} = \mathfrak{g}_{\bar 0} \oplus \mathfrak{g}_{\bar 1}$ has a canonical ideal $\mathfrak{k} = [\mathfrak{g}_{\bar 1}, \mathfrak{g}_{\bar 1}] \oplus \mathfrak{g}_{\bar 1}$, generated by the odd subspace $\mathfrak{g}_{\bar 1}$.

Is there an accepted name for Lie superalgebras for which this ideal is not proper? i.e., for which $\mathfrak{k} = \mathfrak{g}$? In a previous paper I called them odd-generated but I am wondering whether there is an alternative accepted nomenclature.



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