Pennsylvania非局部Hamilton形式、Kohno联络和$\vee$-系统
Purely non-local Hamiltonian formalism, Kohno connections and $\vee$-systems
摘要：
在本文中，我们将纯非局部Hamilton形式主义推广到一类黎曼F-流形，而不需要对乘积$\circ$的半单性或联系$\nabla$的平坦性作任何假设。在平坦的情况下，我们表明，主层次的递归关系可以重新解释使用本地和纯粹的非本地哈密顿算子，在这种情况下，他们分裂成两个Lenard-Magri链，一个涉及偶数项，其他涉及奇数项。此外，我们给出了一个初等的证明，Kohno性质和$\vee$-系统的条件是等价的，在适当的条件下，我们展示了如何关联一个纯粹的非局部哈密顿结构的任何$\vee$-系统，包括退化的。
英文摘要：
In this paper, we extend purely non-local Hamiltonian formalism to a class of Riemannian F-manifolds, without assumptions on the semisimplicity of the product $\circ$ or on the flatness of the connection $\nabla$. In the flat case we show that the recurrence relations for the principal hierarchy can be re-interpreted using a local and purely non-local Hamiltonian operators and in this case they split into two Lenard-Magri chains, one involving the even terms, the other involving the odd terms. Furthermore, we give an elementary proof that the Kohno property and the $\vee$-system condition are equivalent under suitable conditions and we show how to associate a purely non-local Hamiltonian structure to any $\vee$-system, including degenerate ones.
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