论文标题
莫勒 - 卡丹元素集的泊松结构
Poisson structures on sets of Maurer-Cartan elements
论文作者
论文摘要
鉴于满足某些条件的差分分级代数（DGLA），我们在其莫勒 - 卡丹（MC）元素的量规轨道上构建了泊松结构，称为Maurer-Cartan-Poisson（MCP）结构。他们将兼容的Batalin-Vilkovisky代数与L的每个MC元素联系起来。 MCP结构产生了MC元素的哈密顿流动的概念，并在仪表轨道上定义了lie代数，其各向异性代数给出了MC元素的不变式。例如，这给出了与任何封闭的符号歧管相关的有限维度的两步分级分级谎言代数。
Given a differential graded Lie algebra (dgla) L satisfying certain conditions, we construct Poisson structures on the gauge orbits of its set of Maurer-Cartan (MC) elements, termed Maurer-Cartan-Poisson (MCP) structures. They associate a compatible Batalin-Vilkovisky algebra to each MC element of L. An MCP structure is shown to exist for a number of dglas associated to commutative Frobenius algebras, deformations of Poisson and symplectic structures, as well as the Chevally-Eilenberg complex. MCP structures yield a notion of hamiltonian flow of MC elements, and also define Lie algebroids on gauge orbits, whose isotropy algebras give invariants of MC elements. As an example, this gives a finite-dimensional two-step nilpotent graded Lie algebra associated to any closed symplectic manifold.
