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Let $(\mathfrak{g},\tau)$ be a real simple symmetric Lie algebra and let $W\subset \mathfrak{g}$ be an invariant closed convex cone which is pointed andgenerating with $\tau(W) = -W$. For elements $h \in \mathfrak{g}$ with $\tau(h)= h$, we classify the Lie algebras $\mathfrak{g}(W,\tau,h)$ which are generatedby the closed convex cones \[C_{\pm}(W,\tau,h) := (\pm W) \cap\mathfrak{g}_{\pm 1}^{-\tau}(h),\] where $\mathfrak{g}^{-\tau}_{\pm 1}(h) :=\{x \in \mathfrak{g} : \tau(x) = -x, [h,x] = \pm x\}$. These cones occurnaturally as the skew-symmetric parts of the Lie wedges of endomorphismsemigroups of certain standard subspaces. We prove in particular that, if$\mathfrak{g}(W,\tau,h)$ is non-trivial, then it is either a hermitian simpleLie algebra of tube type or a direct sum of two Lie algebras of this type.Moreover, we give for each hermitian simple Lie algebra and each equivalenceclass of involutive automorphisms $\tau$ of $\mathfrak{g}$ with $\tau(W) = -W$a list of possible subalgebras $\mathfrak{g}(W,\tau,h)$ up to isomorphy.

Classification of 3-graded causal subalgebras of real simple Lie algebras