关于Grothendieck-Teichmüller李代数grt_1的下中心序列滤子
On a lower central series filtration of the Grothendieck-Teichmüller Lie algebra grt_1
摘要：
Grothendieck-Teichmüller李代数是自由李代数的导子在两个生成元中的李代数的李子代数。证明了后一种李代数的下中心序列诱导了Grothendieck-Teichmüller李代数的降滤子，并研究了相应的分次李代数.它的零度部分以前由第二作者计算过。我们证明了度1部分是对称代数上的模，这两个部分都具有相容的减滤子，并且我们给出了相应的分次模的一个明确的下界.由此得到Grothendieck-Teichmüller李代数的深度分次的深度3部分的显式表示.
英文摘要：
The Grothendieck-Teichmüller Lie algebra is a Lie subalgebra of a Lie algebra of derivations of the free Lie algebra in two generators. We show that the lower central series of the latter Lie algebra induces a decreasing filtration of the Grothendieck-Teichmüller Lie algebra and we study the corresponding graded Lie algebra. Its degree zero part had been previously computed by the second author. We show that the degree one part is a module over a symmetric algebra, which are both equipped with compatible decreasing filtrations, and we exhibit an explicit lower bound for the associated graded module. We derive from there some information on explicit expression of the depth 3 part of the depth-graded of the Grothendieck-Teichmüller Lie algebra.
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