论文标题
线性符号形式的一致性由符号组组成
Congruence of Linear Symplectic Forms by the Symplectic Group
论文作者
论文摘要
本文涉及线性符号切除术对线性符号形式的作用，通过在偶数上进行结合。我们证明了pfaffian和$ - \ frac {1} {2} \ pereratatorName {tr}（ja）$（sum函数）$ a $的$是不变的。我们使用这些不变性来完整描述尺寸四的轨道空间。此外，我们研究了第四个尺寸的单个轨道的几何形状。在符号几何形状中，我们的分类结果在尺寸四中为$ \ mathbb {r}^{4} $上的两种符号形式提供了必要条件，该条件是通过标准符号形式的符号切除术交织在一起的。这与在差异性下缺乏本地不变性相反。此外，我们确定了一类符号形式的全局不变性，并且我们研究了咖喱 - 列延式稳定性定理的必然性的扩展。最后，我们扩展了结果，并研究了线性符号切除术对尺寸$ 2N $的线性符号形式的作用。我们确定在此操作下的线性符号形式的$ n $不变性，即$ s_k（a）$我们将我们定义为$σ_k（a）$，这是$ tj+a $的pfaffian pfaffian中$ t^k $的系数。
This paper concerns the action of linear symplectomorphisms on linear symplectic forms by conjugation in even dimensions. We prove that pfaffian and $-\frac{1}{2}\operatorname{tr}(JA)$ (sum function) of $A$ are invariants on the action. We use these invariants to provide a complete description of the orbit space in dimension four. In addition, we investigate the geometric shapes of the individual orbits in dimension four. In symplectic geometry, our classification result in dimension four provides a necessary condition for two symplectic forms on $\mathbb{R}^{4}$ to be intertwined by symplectomorphisms of the standard symplectic form. This stands in contrast to the lack of local invariants under diffeomorphisms. Furthermore, we determine global invariants of a class of symplectic forms, and we study an extension of a corollary of the Curry-Pelayo-Tang Stability Theorem. Lastly, we extend our results and investigate the action of linear symplectomorphisms on linear symplectic forms in dimension $2n$. We determine $n$ invariants of linear symplectic forms under this action, namely, $s_k(A)$ we defined as $σ_k(A)$ which is the coefficient of term $t^k$ in the polynomial expansion of pfaffian of $tJ+A$.
