论文标题
Courant代数的较高类似物的线性化
Linearization of the higher analogue of Courant algebroids
论文作者
论文摘要
在本文中，我们表明$ n $ th差速器捆绑包$ \ dev^n e $和$ n $ -th偏斜 - 对称的喷气捆绑$ \ jet_n e $ e $ e $ e $是线性$ n $ n $ n $ n $ n $ $ n $ n $ n $ n $ e^*$ e^*****$ e^***$ e^*$ e^*因此，Bi-Vitagliago-Zhang引入的$ n $ -omni-lie algebroid $ \ dev e \ oplus \ jet_n e $可以解释为某些线性化，我们称之为伪courants $ te^*te^*pe^*pe^*\ oplus \ oplus \ oplus \ wedge的伪线性化。另一方面，我们表明Omni $ n $ -lie algebroid $ \ dev e \ oplus \ wedge^n \ jet E $也可以解释为某些线性化，我们称之为Weinstein-linearization courant courant oplus $ te^*\ oplus \ oplus \ oplus \ oplus \ wedge \ wedge^nt^*e^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^**我们还表明，$ n $ -lie代数，本地$ n $ -lie代数和nambu-jacobi结构可以被描述为Omni $ n $ -lie -Lie代数的可集成子划分。
In this paper, we show that the spaces of sections of the $n$-th differential operator bundle $\dev^n E$ and the $n$-th skew-symmetric jet bundle $\jet_n E$ of a vector bundle $E$ are isomorphic to the spaces of linear $n$-vector fields and linear $n$-forms on $E^*$ respectively. Consequently, the $n$-omni-Lie algebroid $\dev E\oplus\jet_n E$ introduced by Bi-Vitagliago-Zhang can be explained as certain linearization, which we call pseudo-linearization of the higher analogue of Courant algebroids $TE^*\oplus \wedge^nT^*E^*$. On the other hand, we show that the omni $n$-Lie algebroid $\dev E\oplus \wedge^n\jet E$ can also be explained as certain linearization, which we call Weinstein-linearization of the higher analogue of Courant algebroids $TE^*\oplus \wedge^nT^*E^*$. We also show that $n$-Lie algebroids, local $n$-Lie algebras and Nambu-Jacobi structures can be characterized as integrable subbundles of omni $n$-Lie algebroids.
