论文标题
$ l_ \ infty $ - 代数及其同型理论的介绍
An Introduction to $L_\infty$-Algebras and their Homotopy Theory
论文作者
论文摘要
在这篇评论中，我们详细介绍了（弯曲的）$ l_ \ infty $ - algebras和$ l_ \ infty $ - morphimisms的理论。特别是，我们回想起（弯曲的）Maurer-Cartan元素，它们的等效类别和扭曲程序的概念。然后，主要重点是对$ l_ \ infty $ - 代理和$ l_ \ infty $ modules的同质理论的研究。特别是，人们可以将$ l_ \ l_ \ l_ \ infty $ - 模型的$ l_ \ infty $ - 术和形态解释为某些$ l_ \ infty $ -Algebras中的Maurer-cartan元素，我们表明，这表明，这表明将形态扭曲的形态与同等的Maurer-Cartan元素产生同质的同性恋形式。
In this review we give a detailed introduction to the theory of (curved) $L_\infty$-algebras and $L_\infty$-morphisms. In particular, we recall the notion of (curved) Maurer-Cartan elements, their equivalence classes and the twisting procedure. The main focus is then the study of the homotopy theory of $L_\infty$-algebras and $L_\infty$-modules. In particular, one can interpret $L_\infty$-morphisms and morphisms of $L_\infty$-modules as Maurer-Cartan elements in certain $L_\infty$-algebras, and we show that twisting the morphisms with equivalent Maurer-Cartan elements yields homotopic morphisms.
