Dimension filtration on loops
J. Mostovoy, J. M. Pérez-Izquierdo
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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