论文标题
交换性同位代数嵌入非共同同位代数
Commutative homotopical algebra embeds into non-commutative homotopical algebra
论文作者
论文摘要
在一个特征性零的领域，我们表明，来自同型DG代数的同型函数到DG联想代数类别的同型代数类别是忠实的。实际上，诱导的衍生映射空间图可在任何基座上对所有同型组进行注入。我们证明了Unital和非积极代数的类似结果，也证明了来自DG lie代数到DG联想代数的通用包膜函数的Koszul双重结果。一个重要的成分是这些派生的映射空间的自然模型，因为在unitalies中，完整过滤的DG lie代数的Maurer-Cartan空间（或曲面为代数）。
Over a field of characteristic zero, we show that the forgetful functor from the homotopy category of commutative dg algebras to the homotopy category of dg associative algebras is faithful. In fact, the induced map of derived mapping spaces gives an injection on all homotopy groups at any basepoint. We prove similar results both for unital and non-unital algebras, and also Koszul dually for the universal enveloping algebra functor from dg Lie algebras to dg associative algebras. An important ingredient is a natural model for these derived mapping spaces as Maurer-Cartan spaces of complete filtered dg Lie algebras (or curved Lie algebras, in the unital case).
