论文标题
（-1）缩短衍生的泊松歧管的量化
Quantization of (-1)-Shifted Derived Poisson Manifolds
论文作者
论文摘要
我们研究了$（1）$ - 移动的衍生泊松歧管的量化问题，该poisson歧管在Berezinian半浓度的空间上的$ \ bv_ \ infty $ operators。我们证明，量化这种$（ - 1）$ - 移动的衍生泊森歧管等同于抬起差异分级的短序列的莫拉勒 - 卡丹元素的连续序列，其中障碍物是第二多泊松同学中的某些类别的障碍物。因此，如果第二个Poisson共同体学组消失，则可以量化$（1）$ - 转移的衍生泊松歧管。我们还证明，对于任何$ a $ -AlgeBroid $ \ cc {\ av} $，其相应的线性$（ - 1）$ - 移位派生的poisson歧管$ \ cc {\ av}^\ vee [-1] $接受一个规范的量化。最后，鉴于谎言代数$ a $和一个单一循环的$ s \ in \ in \ excontions {a^\ vee} $，$（ - 1）$ - 移动的派生的poisson poisson coistropic submanifolds的衍生相交的相互作用，由$ s $ s $ s $ s $ s $ s $ s $ s $ s lie poisson $ poisson $ a^lie poisson $ a^lie poisson $ a^A^lie poisson $ a^A^lie poisson $ a^就evens-lu-weinstein模块而言。
We investigate the quantization problem of $(-1)$-shifted derived Poisson manifolds in terms of $\BV_\infty$-operators on the space of Berezinian half-densities. We prove that quantizing such a $(-1)$-shifted derived Poisson manifold is equivalent to the lifting of a consecutive sequences of Maurer-Cartan elements of short exact sequences of differential graded Lie algebras, where the obstruction is a certain class in the second Poisson cohomology. Consequently, a $(-1)$-shifted derived Poisson manifold is quantizable if the second Poisson cohomology group vanishes. We also prove that for any $Ł$-algebroid $\Cc{\aV}$, its corresponding linear $(-1)$-shifted derived Poisson manifold $\Cc{\aV}^\vee[-1]$ admits a canonical quantization. Finally, given a Lie algebroid $A$ and a one-cocycle $s\in \sections{A^\vee}$, the $(-1)$-shifted derived Poisson manifold corresponding to the derived intersection of coisotropic submanifolds determined by the graph of $s$ and the zero section of the Lie Poisson $A^\vee$ is shown to admit a canonical quantization in terms of Evens-Lu-Weinstein module.
