论文标题
矢量场的不可及其超级分子
Transitive irreducible Lie superalgebras of vector fields
论文作者
论文摘要
令$ \ mathfrak {d} $为均质矢量束$ e $ y $ g/p $ y $ g/g $，其中$ g $是一个简单的有限型二级复合体组和$ p $ p $ parabolic子组。然后，$ \ mathfrak {d} $是不可约$ p $ -module $ v $定义$ e $的$ e $时的传递性和不可约的。此外，$ \ mathfrak {d} $很简单;这是超级点上矢量场的谎言超级甲壳虫的同构，即$ 0 | n $维度的监督。
Let $\mathfrak{d}$ be the Lie superalgebra of superderivations of the sheaf of sections of the exterior algebra of the homogeneous vector bundle $E$ over the flag variety $G/P$, where $G$ is a simple finite-dimensional complex Lie group and $P$ its parabolic subgroup. Then, $\mathfrak{d}$ is transitive and irreducible whenever $E$ is defined by an irreducible $P$-module $V$ such that the highest weight of $V^*$ is dominant. Moreover, $\mathfrak{d}$ is simple; it is isomorphic to the Lie superalgebra of vector fields on the superpoint, i.e., on a $0|n$-dimensional supervariety.
