论文标题
较高的多国代数
Higher Multi-Courant Algebroids
论文作者
论文摘要
$（e，\ langle \ cdot，\ cdot \ rangle）$的courant代数结构的二进制支架可以扩展到$γ（e）$上的$ n $ - ary式托架，从而产生多种用词汇剂。这些$ n $ - ary括号形成了泊松代数，并在代数环境中定义了凯勒和沃尔德曼。我们构建了Keller-Waldmann Poisson代数的较高几何版本，并定义了较高的多国代数。由于courant代数结构可以看作是度数$ 3 $函数的$ 3 $函数$ 2 $ $ 2 $，因此可以将较高的多委员会结构视为该分级符号歧管上$ n \ geq 3 $的功能。
The binary bracket of a Courant algebroid structure on $(E,\langle \cdot,\cdot \rangle)$ can be extended to a $n$-ary bracket on $Γ(E)$, yielding a multi-Courant algebroid. These $n$-ary brackets form a Poisson algebra and were defined, in an algebraic setting, by Keller and Waldmann. We construct a higher geometric version of Keller-Waldmann Poisson algebra and define higher multi-Courant algebroids. As Courant algebroid structures can be seen as degree $3$ functions on a graded symplectic manifold of degree $2$, higher multi-Courant structures can be seen as functions of degree $n\geq 3$ on that graded symplectic manifold.
