论文标题
派生的Poincaré-Birkhoff-Witt定理（带有Vladimir Dotsenko的附录）
Derived Poincaré-Birkhoff-Witt theorems (with an appendix by Vladimir Dotsenko)
论文作者
论文摘要
我们定义了派生的庞卡 - birkhoff-简称DG Opirad或派生的PBW地图，该地图扩展了V.〜Dotsenko的Operads和1804.06485的第二作者之间的PBW地图的定义，目的是研究通用的Algebra of DG lie Alge lie Algebras作为一个功能范围的室内。我们的主要结果表明，从同质性谎言到同型协会的地图是派生的，这使我们对$ l_ \ infty $ -Algebra的通用信封的同源性说明了lada-markl的意义。 We deduce from this several known results involving universal envelopes of $L_\infty$-algebras of V. Baranovsky and J. Moreno-Fernández, and extend D. Quillen's classical quasi-isomorphism $\mathcal C \longrightarrow BU$ from dg Lie algebras to $L_\infty$-algebras;这证实了J. Moreno-Fernández的猜想。
We define derived Poincaré--Birkhoff--Witt maps of dg operads or derived PBW maps, for short, which extend the definition of PBW maps between operads of V.~Dotsenko and the second author in 1804.06485, with the purpose of studying the universal enveloping algebra of dg Lie algebras as a functor on the homotopy category. Our main result shows that the map from the homotopy Lie operad to the homotopy associative operad is derived PBW, which gives us an amenable description of the homology of the universal envelope of an $L_\infty$-algebra in the sense of Lada--Markl. We deduce from this several known results involving universal envelopes of $L_\infty$-algebras of V. Baranovsky and J. Moreno-Fernández, and extend D. Quillen's classical quasi-isomorphism $\mathcal C \longrightarrow BU$ from dg Lie algebras to $L_\infty$-algebras; this confirms a conjecture of J. Moreno-Fernández.
