从循环图构造乘积图变分种可积系统
Integrable systems on multiplicative quiver varieties from cyclic quivers
AI总结：
本文通过构造乘积图变种的泊松子代数，提出了一种新的自旋Ruijsenaars-Schneider系统的可积系统泛化方法。
摘要：
我们考虑一类复流形，其构造为与一个扩展了任意数量箭头的循环图相关的乘积图变种。此类变种具有泊松结构，该结构通过准哈密顿约简获得。我们构建了几个家庭的泊松子代数，这些子代数位于这些空间的坐标环内，我们用它们来获得退化可积系统。我们还扩展了这些代数的泊松中心到最大阿贝尔泊松代数，从而定义了刘维尔可积系统。通过考虑乘积图变种上的适当局部坐标集，我们可以显式推导出局部泊松结构。这使我们能够将所构建的可积系统解释为新的具有多种自旋变量的自旋Ruijsenaars-Schneider系统的泛化。
英文摘要：
We consider a class of complex manifolds constructed as multiplicative quiver varieties associated with a cyclic quiver extended by an arbitrary number of arrows starting at a new vertex. Such varieties admit a Poisson structure, which is obtained by quasi-Hamiltonian reduction. We construct several families of Poisson subalgebras inside the coordinate ring of these spaces, which we use to obtain degenerately integrable systems. We also extend the Poisson centre of these algebras to maximal abelian Poisson algebras, hence defining Liouville integrable systems. By considering a suitable set of local coordinates on the multiplicative quiver varieties, we can derive the local Poisson structure explicitly. This allows us to interpret the integrable systems that we have constructed as new generalisations of the spin Ruijsenaars-Schneider system with several types of spin variables.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
