论文标题
部分可观测时空混沌系统的无模型预测
Rigidity results for Lie algebras admitting a post-Lie algebra structure
论文作者
论文摘要
我们研究成对的谎言代数$（\ mathfrak {g}，\ mathfrak {n}）的刚性问题。我们表明，如果$ \ mathfrak {g} $是半完整的，而$ \ mathfrak {n} $是任意的，那么从某种意义上说，$ \ mathfrak {g} $和$ \ mathfrak {n} $必须是异，我们具有刚性。证明使用lie代数$ \ mathfrak {g} = \ mathfrak {s} _1 \ dotplus \ mathfrak {s} _2 $作为直接矢量空间总和的两个半imimple subgebras的直接矢量空间总和。我们表明，$ \ mathfrak {g} $必须是半imple，因此与直接谎言代数$ \ mathfrak {g} \ cong \ mathfrak {s} _1 \ oplus \ oplus \ mathfrak {s}} _2 $。这解决了在lie代数$（\ mathfrak {g}，\ mathfrak {n}）$成对上的lie lie代数结构的一些开放存在问题。我们证明了对$（\ mathfrak {g}，\ mathfrak {n}）$的其他存在结果，其中$ \ mathfrak {g} $是完整的，对成对，其中$ \ mathfrak {g} $是还原的，是$ 1 $ dimensional Center中心和$ \ Mathfrak and $ \ mathfrak nilp solt nil的$ 1 $ -Dimensional Center Center中心和$ \ Mathfrak。
We study rigidity questions for pairs of Lie algebras $(\mathfrak{g},\mathfrak{n})$ admitting a post-Lie algebra structure. We show that if $\mathfrak{g}$ is semisimple and $\mathfrak{n}$ is arbitrary, then we have rigidity in the sense that $\mathfrak{g}$ and $\mathfrak{n}$ must be isomorphic. The proof uses a result on the decomposition of a Lie algebra $\mathfrak{g}=\mathfrak{s}_1\dotplus \mathfrak{s}_2$ as the direct vector space sum of two semisimple subalgebras. We show that $\mathfrak{g}$ must be semisimple and hence isomorphic to the direct Lie algebra sum $\mathfrak{g}\cong \mathfrak{s}_1\oplus \mathfrak{s}_2$. This solves some open existence questions for post-Lie algebra structures on pairs of Lie algebras $(\mathfrak{g},\mathfrak{n})$. We prove additional existence results for pairs $(\mathfrak{g},\mathfrak{n})$, where $\mathfrak{g}$ is complete, and for pairs, where $\mathfrak{g}$ is reductive with $1$-dimensional center and $\mathfrak{n}$ is solvable or nilpotent.
