论文标题
DG-LIE代数上模型结构的基本方法
An elementary approach to the model structure on DG-Lie algebras
论文作者
论文摘要
本文包含一个基本证据，证明了经典模型结构在特征零领域的无界DG-LIE代数类别上的存在，重点是自由和半空扩展的特性，这是特别好的联合启动。局部相结合的共同煤层的cobar构造被证明是半级DG-lie代数的一个例子。我们还举例说明了一个非成熟的DG-lie代数，其基本分级的谎言代数是免费的。这不能在上述情况下发生，在这种情况下，这种形式的DG-lie代数始终是同伴的。
This paper contains an elementary proof of the existence of the classical model structure on the category of unbounded DG-Lie algebras over a field of characteristic zero, with an emphasis on the properties of free and semifree extensions, which are particularly nice cofibrations. The cobar construction of a locally conilpotent cocommutative coalgebra is shown to be an example of semifree DG-Lie algebra. We also give an example of a non-cofibrant DG-Lie algebra whose underlying graded Lie algebra is free; this cannot occur in the bounded above case, where DG-Lie algebras of this form are always cofibrant.
