标题： 移位的双重泊松结构和非交换泊松扩张 显示英文标题

标题： Shifted double Poisson structures and noncommutative Poisson extensions

摘要： 我们发展了非交换泊松扩张的理论。 对于一个增广的微分分次代数\(A\)，我们证明了\(A\)上的任何移位双泊松括号都会在约化循环同调上诱导出一个分次李代数结构。 在 Kontsevich--Rosenberg 原则下，我们进一步证明非交换泊松扩张与非交换哈密顿约化是相容的。 此外，我们证明了移位双泊松结构独立于余挠分解的选择，并且它们在表示的导出模空间上诱导出移位泊松结构。 显示英文摘要

摘要： We develop a theory of noncommutative Poisson extensions. For an augmented dg algebra \(A\), we show that any shifted double Poisson bracket on \(A\) induces a graded Lie algebra structure on the reduced cyclic homology. Under the Kontsevich--Rosenberg principle, we further prove that the noncommutative Poisson extension is compatible with noncommutative Hamiltonian reduction. Moreover, we show that shifted double Poisson structures are independent of the choice of cofibrant resolutions and that they induce shifted Poisson structures on the derived moduli stack of representations.