论文标题
准泊松结构，弱的准汉密尔顿结构和各种模量空间的泊松几何形状
Quasi Poisson structures, weakly quasi Hamiltonian structures, and Poisson geometry of various moduli spaces
论文作者
论文摘要
让G成为一个谎言组，G谎言代数。我们在G的张张平方和一般不一定不一定不一定非脱位的准汉密尔顿结构中，相对于不一定不一定是非偏置的a dement poiss poiss poiss poiss poiss poiss poiss poiss se，我们开发了相对于不一定不一定不一定不一定非脱位的对称的2张量相对于不一定非脱位的对称的2张量的理论的理论。用G作为对称组定义的数据涉及2张量测量该括号如何无法满足雅各比身份。目前的方法涉及一个新颖的动量映射和产量的概念，在非脱位情况下，非分类的准泊松结构与非分类的准汉密尔顿结构之间的徒点对应关系。新理论适用于各种非单明模量空间，并通过还原相对于适当定义的动量映射，而不一定是非分类的普通泊松结构。在这些模量空间中，有可能被刺穿的基本组的表示空间，可能是扭曲的。在非分类的情况下，这种泊松结构归结为文献中探讨的一种分层的符合性的结构，例如，narasimhan和seshadri引入了Kähler结构的符号部分，该部分是由稳定的Holomorphic矢量载体载体载体载体载体的模量空间。在代数环境中，这些模量空间不一定是非象征性仿射不一定是非分类泊松品种。一个侧面结果是与仪表理论无关的扩展模量空间与准汉密尔顿空间之间的明显等效性。
Let G be a Lie group and g its Lie algebra. We develop a theory of quasi Poisson structures relative to a not necessarily non-degenerate Ad-invariant symmetric 2-tensor in the tensor square of g and one of general not necessarily non-degenerate quasi Hamiltonian structures relative to a not necessarily non-degenerate Ad-invariant symmetric bilinear form on g, a quasi Poisson structure being given by a skew bracket of two variables such that suitable data defined in terms of G as symmetry group involving the 2-tensor measure how that bracket fails to satisfy the Jacobi identity. The present approach involves a novel concept of momentum mapping and yields, in the non-degenerate case, a bijective correspondence between non-degenerate quasi Poisson structures and non-degenerate quasi Hamiltonian structures. The new theory applies to various not necessarily non-singular moduli spaces and yields thereupon, via reduction with respect to an appropriately defined momentum mapping, not necessarily non-degenerate ordinary Poisson structures. Among these moduli spaces are representation spaces, possibly twisted, of the fundamental group of a Riemann surface, possibly punctured, and moduli spaces of semistable holomorphic vector bundles as well as Higgs bundle moduli spaces. In the non-degenerate case, such a Poisson structure comes down to a stratified symplectic one of the kind explored in the literature and recovers, e.g., the symplectic part of a Kähler structure introduced by Narasimhan and Seshadri for moduli spaces of stable holomorphic vector bundles on a curve. In the algebraic setting, these moduli spaces arise as not necessarily non-singular affine not necessarily non-degenerate Poisson varieties. A side result is an explicit equivalence between extended moduli spaces and quasi Hamiltonian spaces independently of gauge theory.
