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Dimension filtration on loops

J. Mostovoy·J. M. Pérez-Izquierdo
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Abstract

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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J. Mostovoy, J. M. Pérez-Izquierdo. 2004-10-24. Dimension filtration on loops. https://arxiv.org/abs/math/0410516

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