变形理论（课堂讲稿）
Deformation Theory (lecture notes)
摘要：
本文的前三部分概述了结合代数的变形理论的经典主题和必要的背景材料。然后，我们分析的Hochschild上同调的代数结构，并描述相应的Maurer-Cartan方程的变形和解决方案之间的关系。第六节将Maurer-Cartan方程推广到强同伦李代数上，证明了该方程解的模空间的同伦不变性。在最后一节中，我们指出的主要思想Kontsevich的证明存在的变形量子化的泊松流形。
英文摘要：
First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation between deformations and solutions of the corresponding Maurer-Cartan equation. In Section 6 we generalize the Maurer-Cartan equation to strongly homotopy Lie algebras and prove the homotopy invariance of the moduli space of solutions of this equation. In the last section we indicate the main ideas of Kontsevich's proof of the existence of deformation quantization of Poisson manifolds.
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