The notion of lower central series for loops

被引：0

作者：

Mostovoy, J ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Unidad Cuernavaca, Mexico City 04510, DF, Mexico

来源：

Non-Associative Algebra and Its Applications | 2006年 / 246卷

关键词：

loop; commutator-associator filtration; lower central series;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The commutator calculus is one of the basic tools in group theory. However, its extension to the nonassociative context, based on the usual definition of the lower central series of a loop, is not entirely satisfactory. Namely, the graded abelian group associated to the lower central series of a loop is not known to carry any interesting algebraic structure. In this note we construct a new generalization of the lower central series to arbitrary loops that is tailored to produce a set of multilinear operations on the associated graded group.

引用

页码：291 / 298

页数：8