Let (\( \mathfrak{g} \), τ) be a real simple symmetric Lie algebra and let W ⊂ \( \mathfrak{g} \) be an invariant closed convex cone which is pointed and generating with τ(W) = −W. For elements h ∈ \( \mathfrak{g} \) with τ(h) = h, we classify the Lie algebras \( \mathfrak{g} \)(W, τ, h) which are generated by the closed convex cones \( {C}_{\pm}\left(W,\tau, h\right):= \left(\pm W\right)\cap {\mathfrak{g}}_{\pm 1}^{-\tau }(h) \), where \( {\mathfrak{g}}_{\pm 1}^{-\tau }(h):= \left\{x\in \mathfrak{g}:\tau (x)=-x\left[h,x\right]=\pm x\right\} \). These cones occur naturally as the skew-symmetric parts of the Lie wedges of endomorphism semigroups of certain standard subspaces. We prove in particular that, if \( \mathfrak{g} \)(W, τ, h) is non-trivial, then it is either a hermitian simple Lie 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 equivalence class of involutive automorphisms τ of \( \mathfrak{g} \) with τ(W) = −W a list of possible subalgebras \( \mathfrak{g} \)(W, τ, h) up to isomorphy.

让（\（\ mathfrak {G} \），τ）是一个真正简单的对称李代数和让W¯¯ ⊂ \（\ mathfrak {G} \）是不变的封闭凸锥是尖并产生与τ（w ^） = -W。对于元件ħ ∈ \（\ mathfrak {G} \）与τ（ħ）= ^ h，我们分类的李代数\（\ mathfrak {G} \） （w ^，τ，ħ其由闭凸锥体产生）\（{C} _ {\ pm} \ left（W，\ tau，h \ right）：= \ left（\ pm W \ right）\ cap {\ mathfrak {g}} _ {\ pm 1} ^ { -\ tau}（h）\），其中\（{\ mathfrak {g}} _ {\ pm 1} ^ {-\ tau}（h）：= \ left \ {x \ in \ mathfrak {g}： \ tau（x）=-x \ left [h，x \ right] = \ pm x \ right \} \）。这些锥体自然地作为某些标准子空间的内同态半群的Lie楔形的倾斜对称部分出现。我们特别证明，如果\（\ mathfrak {g} \）（W，τ，h）是非平凡的，则它要么是管状的Hermitian简单Lie代数，要么是该类型的两个Lie代数的直接和。类型。此外，我们给每个埃尔米特简单李代数和每个等价类对合构的τ的\（\ mathfrak {g} \）且τ（W）= − W直到同构的可能子代数\（\ mathfrak {g} \）（W，τ，h）的列表。