Dimension filtration on loops

Details Dimension filtration on loops Dimension filtration on loops

2004-10-24

arxiv.org/abs/math/0410516v1

Mathematics

Group Theory

8 pages

Scientific paper

We show that the graded group associated to the dimension filtration on a
loop acquires the structure of a Sabinin algebra after being tensored with a
field of characteristic zero. The key to the proof is the interpretation of the
primitive operations of Umirbaev and Shestakov in terms of the operations on a
loop that measure the failure of the associator to be a homomorphism.

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