Institute for Mathematical Physics Dirac Geometry, Quasi–poisson Actions and D/g–valued Moment Maps Dirac Geometry, Quasi-poisson Actions and D/g-valued Moment Maps
Institute for Mathematical Physics Dirac Geometry, Quasi–poisson Actions and D/g–valued Moment Maps Dirac Geometry, Quasi-poisson Actions and D/g-valued Moment Maps
复制标题
DOI：
--
复制
发表时间：
--
期刊：
影响因子：
--
通讯作者：
H. Bursztyn;M. Crainic
中科院分区：
文献类型：
--
作者：
H. Bursztyn;M. Crainic
我们研究与马宁对 (d, g) 相关的狄拉克结构，并给出具有 D/G 值矩图的哈密顿空间的狄拉克几何方法，最初由 Alekseev 和 Kosmann-Schwarzbach [3] 在准泊松结构方面引入。我们解释这两个不同的框架如何相互关联，证明它们导致哈密顿空间的同构类别。我们强调狄拉克几何观点与等变微分形式之间的联系。本文讨论了各种示例，包括 q-哈密尔顿空间和泊松-李群作用，解释了前辛群胚如何与每种情况下的“双”概念相关。
We study Dirac structures associated with Manin pairs (d, g) and give a Dirac geometric approach to Hamiltonian spaces with D/G-valued moment maps, originally introduced by Alekseev and Kosmann-Schwarzbach [3] in terms of quasi-Poisson structures. We explain how these two distinct frameworks are related to each other, proving that they lead to isomorphic categories of Hamiltonian spaces. We stress the connection between the viewpoint of Dirac geometry and equivariant differential forms. The paper discusses various examples, including q-Hamiltonian spaces and Poisson-Lie group actions, explaining how presymplectic groupoids are related to the notion of " double " in each context.