论文标题
dirac生成courant代数的操作员
Dirac generating operators of split Courant algebroids
论文作者
论文摘要
给定一个向量捆绑包$ a $在平滑的歧管上$ m $上，以使线束的平方根$ \ mathcal {l} $的线束$ \ wedge^{\ mathrm {top}} a^\ ast \ ast \ ast \ ast \ ast \ wedge \ wedge^wedge^{\ mathrm {\ top}}伪euclidean vector bundle $（e = a \ oplus a^\ ast，\ langle \ cdot，\ cdot \ rangle）$，承认一个旋转纺纱$ \ wedge^\ wedge^\ bullet a \ ot a \ ot a \ ot a \ otimimimimimimimimimime \ nathcal {l} $，其部分可以被散布的空间，该杂志的空间是贝尔氏群落的， $ a^\ ast [1] $。我们在Alekseev和Xu引入的$ a \ oplus a^\ ast $上，对分裂的代数（或原始晶状体）结构进行了明确的结构。我们还证明，狄拉克生成操作员的正方形产生了分裂的代数代数的不变性。
Given a vector bundle $A$ over a smooth manifold $M$ such that the square root $\mathcal{L}$ of the line bundle $\wedge^{\mathrm{top}}A^\ast \otimes \wedge^{\mathrm{top}}T^\ast M$ exists, the Clifford bundle associated to the split pseudo-Euclidean vector bundle $(E = A \oplus A^\ast, \langle \cdot, \cdot \rangle)$, admits a spinor bundle $\wedge^\bullet A \otimes \mathcal{L}$, whose section space can be thought of as that of Berezinian half-densities of the graded manifold $A^\ast[1]$. We give an explicit construction of Dirac generating operators of split Courant algebroid (or proto-bialgebroid) structures on $A \oplus A^\ast$ introduced by Alekseev and Xu. We also prove that the square of the Dirac generating operator gives rise to an invariant of the split Courant algebroid.
