论文标题
实现谎言超级g（3）和f（4）作为超切地理的对称性的实现
Realization of Lie superalgebras G(3) and F(4) as symmetries of supergeometries
论文作者
论文摘要
对于每个抛物线亚组$ p $ a Lie SuperGroup $ g $的均质超空间$ g/p $带有$ g $ invariant超级几何。如果$ \ mathfrak {g} = \ operatorName {lie}（g）$是Quesiton，这是此超单几何的最大对称性。我们的方法是考虑每种选择抛物面的否定分级超级甲壳虫，并计算田中 - 韦利弗尔延长的延长，并在需要时减少结构组（2个resp 3案例），从而意识到$ g（3）$和$ f（3）$和$ f（4）$作为Supergeometries的对称性。这给出了19个不等的$ g（3）$ - 超级地理位序和55个不相等的$ f（4）$ - 超级地理位置，在大多数情况下（17例RESP 52案例），这些案例被编码为矢量超级分布。我们在某些情况下描述了这些超晶状体，并明确地实现超对称性。
For every parabolic subgroup $P$ of a Lie supergroup $G$ the homogeneous superspace $G/P$ carries a $G$-invariant supergeometry. We address the quesiton whether $\mathfrak{g}=\operatorname{Lie}(G)$ is the maximal symmetry of this supergeometry in the case of exceptional Lie superalgebras $G(3)$ and $F(4)$. Our approach is to consider the negatively graded Lie superalgebras for every choice of parabolic, and to compute the Tanaka-Weisfeiler prolongations, with reduction of the structure group when required (2 resp 3 cases), thus realizing $G(3)$ and $F(4)$ as symmetries of supergeometries. This gives 19 inequivalent $G(3)$-supergeometries and 55 inequivalent $F(4)$-supergeometries, in majority of cases (17 resp 52 cases) those being encoded as vector superdistributions. We describe those supergeometries and realize supersymmetry explicitly in some cases.
