斯宾塞上同调与多辛结构的可积性
The Spencer cohomology and integrability of multisymplectic structures
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中文总结 AI 辅助
通过将多辛结构识别为G - 结构研究其可积性问题，运用斯宾塞上同调理论给出多辛形式在常系数图表下的条件，对常线性型多辛结构分类，还给出证明达布定理的方案及构建特定多辛形式等。
中文摘要 AI 辅助
我们通过将多辛结构识别为G - 结构来研究多辛结构的可积性问题。应用斯宾塞上同调理论，我们给出了多辛形式在允许具有常系数的图表中的条件。这种一般性研究允许根据稳定子群的自然作用对常线性型多辛结构进行粗略分类。该理论通过提供一个证明达布定理的方案来说明，并以几个相关案例为例。我们还构建了多辛形式$\varpi_j$的线性型，其平坦性严格要求j阶条件。最后，在场论的情况下计算了相应的李代数。
英文摘要
We study the integrability problem of multisymplectic structures, by identifying them as $G$-structures. Applying the theory of Spencer cohomology, we give conditions on a multisymplectic form for it to admit a chart in which it has constant coefficients. This general study allows for a rough classification of multisymplectic structures of constant linear type, depending on the natural action of the stabilizer group. The theory is illustrated by providing a scheme for proving a Darboux theorem, which is exemplified with several relevant cases. We also build linear types of multisymplectic forms $\varpi_j$ whose flatness strictly requires a condition of order $j$. Finally, the corresponding Lie algebras are computed in the case of field theories.
