论文标题
可观察到多链歧管和较高的courant代数
Observables on multisymplectic manifolds and higher Courant algebroids
论文作者
论文摘要
令$ω$为任意程度的封闭式非分类差异形式。与之相关的是一个$ l _ {\ infty} $ - 可观察的代数，还有$ l _ {\ infty} $ - 较高courant algebroid twist twist $ω$的较高代数的部分。我们的主要结果是存在$ l _ {\ infty} $ - 将前者嵌入后者中。我们为嵌入式显示涉及伯努利号码的明确公式。当$ω$是一种不可或缺的符号形式时，可以通过前后化结构几何地实现嵌入，并且当$ω$是3型的3型时，Rogers在2010年发现了嵌入。此外，在存在同型矩图的情况下，我们显示嵌入与仪表转换相吻合。
Let $ω$ be a closed, non-degenerate differential form of arbitrary degree. Associated to it there are an $L_{\infty}$-algebra of observables, and an $L_{\infty}$-algebra of sections of the higher Courant algebroid twisted by $ω$. Our main result is the existence of an $L_{\infty}$-embedding of the former into the latter. We display explicit formulae for the embedding, involving the Bernoulli numbers. When $ω$ is an integral symplectic form, the embedding can be realized geometrically via the prequantization construction, and when $ω$ is a 3-form the embedding was found by Rogers in 2010. Further, in the presence of homotopy moment maps, we show that the embedding is compatible with gauge transformations.
