We construct an infinite-dimensional Lie rackoid Y which hosts an integration of the standard Courant algebroid. As a set, $$Y={{\mathcal {C}}}^{\infty }([0,1],T^*M)$$ Y = C ∞ ( [ 0 , 1 ] , T ∗ M ) for a compact manifold M . The rackoid product is by automorphisms of the Dorfman bracket. The first part of the article is a study of the Lie rackoid Y and its tangent Leibniz algebroid, a quotient of which is the standard Courant algebroid. In the second part, we study the equivalence relation related to the quotient on the rackoid level and restrict then to an integrable Dirac structure. We show how our integrating object contains the corresponding integrating Weinstein Lie groupoid in the case where the Dirac structure is given by a Poisson structure.

中文翻译：

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Lie rackoids 集成 Courant 代数

我们构造了一个无限维的 Lie rackoid Y，它承载了标准 Courant 代数的积分。作为一个集合，$$Y={{\mathcal {C}}}^{\infty }([0,1],T^*M)$$ Y = C ∞ ( [ 0 , 1 ] , T ∗ M ) 对于紧凑流形 M 。齿条积是由 Dorfman 支架的自同构产生的。文章的第一部分是对Lie rackoid Y 及其切线Leibniz algebroid 的研究，其中的商是标准Courant algebroid。在第二部分中，我们研究了与齿条水平商相关的等价关系，并将其限制为可积狄拉克结构。我们展示了在狄拉克结构由泊松结构给出的情况下，我们的积分对象如何包含相应的积分 Weinstein Lie groupoid。