论文标题
可允许的谎言代数中标准子空间的内态分数楔形楔
Lie wedges of endomorphism semigroups of standard subspaces in admissible Lie algebras
论文作者
论文摘要
令$ \ mathfrak {g} $为一个真正的有限维谎言代数，包含尖的生成不变的封闭凸锥。我们确定$ \ mathfrak {g} $的$ d $ d $ d $ of $ \ mathfrak {g} = \ mathfrak {g} _ { - 1} \ oplus \ mathfrak \ mathfrak {g} _0 \ oplus \ oplus \ mathfrak g} $ _1 $（\ pm 1）$ - eigenspaces $ \ mathfrak {g} _ {\ pm 1} $ $ d $的$ d $是由与形式$ w = \ mathcal {o} _f^*$的形式的生成锥产生的\ Mathfrak {Z}（\ Mathfrak {G}）^*$和$ \ Mathcal {o} _f^*$是$ \ Mathcal {O} _f $的双锥。特别是，我们表明，如果$ \ mathfrak {g} $是可解决的，则没有这种衍生，除了存在琐碎的衍生物。 这延续了我们对标准子空间的内态半群的谎言楔子产生的谎言代数的分类。该分类是由标准子空间与代数量子场理论中von Neumann代数的Haag-Kastler网的网络之间的关系。
Let $\mathfrak{g}$ be a real finite-dimensional Lie algebra containing pointed generating invariant closed convex cones. We determine those derivations $D$ of $\mathfrak{g}$ which induce a 3-grading of the form $\mathfrak{g} = \mathfrak{g}_{-1} \oplus \mathfrak{g}_0 \oplus \mathfrak{g}_1$ on $\mathfrak{g}$ such that the $(\pm 1)$-eigenspaces $\mathfrak{g}_{\pm 1}$ of $D$ are generated by the intersections with generating cones of the form $W = \mathcal{O}_f^*$, where $\mathcal{O}_f$ is the coadjoint orbit of a linear functional $f \in \mathfrak{z}(\mathfrak{g})^*$ and $\mathcal{O}_f^*$ is the dual cone of $\mathcal{O}_f$. In particular, we show that, if $\mathfrak{g}$ is solvable, no such derivation except the trivial one exists. This continues our classification of Lie algebras generated by Lie wedges of endomorphism semigroups of standard subspaces. The classification is motivated by the relation of nets of standard subspaces to Haag-Kastler nets of von Neumann algebras in Algebraic Quantum Field Theory.
