论文标题
实际简单谎言代数的三级因果亚代代代数分类
Classification of 3-graded causal subalgebras of real simple Lie algebras
论文作者
论文摘要
令$（\ mathfrak {g}，τ）$为一个真正的简单对称谎言代数，让$ w \ subset \ mathfrak {g} $是一个不变的封闭凸锥，它指向并以$τ（w）= -w $生成。对于$ h \ in \ mathfrak {g} $的元素，$τ（h）= h $，我们对lie代数$ \ mathfrak {g}（w，w，τ，h）$进行了分类，这些$ \ [w，τ，h）$由封闭的convex cones \ [c _ {c _ {\ pm}（\ pm}（w，w，τ，h） \ Mathfrak {g} _ {\ pm 1}^{ - τ}（h），\]，其中$ \ mathfrak {g}^{ - _ { - τ} _ {\ pm 1}（h）：= \ \ \ \ \ \ \ {x \ {x \ {x \ in \ mathfrak in \ mathfrak {g}：f}：f}这些锥体自然出现在某些标准子空间的内态半群的lie楔形楔形部分。我们特别证明，如果$ \ mathfrak {g}（w，τ，h）$是非平凡的，那么它是管类型的Hermitian简单的Lie代数，或者是这种类型的两个lie代数的直接总和。此外，我们为每个Hermitian简单的谎言代数和每个等效类别的自动形态类别$ \ Mathfrak $ \ Mathfrak {g} $，带有$τ（w）= -w $列出可能的subalgebras $ \ mathfrak $ \ mathfrak {g}（g}（w，w，τ，h）$ to Isomorphy。
Let $(\mathfrak{g},τ)$ be a real simple symmetric Lie algebra and let $W \subset \mathfrak{g}$ be an invariant closed convex cone which is pointed and generating with $τ(W) = -W$. For elements $h \in \mathfrak{g}$ with $τ(h) = h$, we classify the Lie algebras $\mathfrak{g}(W,τ,h)$ which are generated by the closed convex cones \[C_{\pm}(W,τ,h) := (\pm W) \cap \mathfrak{g}_{\pm 1}^{-τ}(h),\] where $\mathfrak{g}^{-τ}_{\pm 1}(h) := \{x \in \mathfrak{g} : τ(x) = -x, [h,x] = \pm x\}$. 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.
