论文标题
Nielsen-Schreier品种的有效标准
An effective criterion for Nielsen-Schreier varieties
论文作者
论文摘要
如果一个自由代数的每个子代数都是自由的，则据说某种类型的所有代数都会形成Nielsen-Schreier品种。该物业被认为是极为罕见的。特别是，在此主题的先前工作中，只发现了六个具有二进制操作的代数的Nielsen-Schreier品种。我们在代数特征的情况下提出了尼尔森 - 雪松属性的有效组合标准。在我们的方法中，Operads扮演着至关重要的角色。使用此标准，我们表明，所有前代代数和所有可行的代数的众所周知的品种都是Nielsen-Schreier，而且非常令人惊讶的是，已经有许多具有无数等量的Nielsen-Schreier schreier schreier，具有一个具有一个Binary Operation and Lection and Lecim four的代数。
All algebras of a certain type are said to form a Nielsen-Schreier variety if every subalgebra of a free algebra is free. This property has been perceived as extremely rare; in particular, only six Nielsen-Schreier varieties of algebras with one binary operation have been discovered in prior work on this topic. We propose an effective combinatorial criterion for the Nielsen-Schreier property in the case of algebras over a field of zero characteristic; in our approach, operads play a crucial role. Using this criterion, we show that the well known varieties of all pre-Lie algebras and of all Lie-admissible algebras are Nielsen-Schreier, and, quite surprisingly, that there are already infinitely many non-equivalent Nielsen-Schreier varieties of algebras with one binary operation and identities of degree four.
