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Dimension filtration on loops

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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 Shestakov and Umirbaev in terms of the operations on a loop that measure the failure of the associator to be a homomorphism.

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Authors and Affiliations

  1. Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, A.P. 273-3, C.P. 62251, Cuernavaca, Morelos, Mexico

    J. Mostovoy

  2. Departamento Matemáticas y Computación, Universidad de La Rioja, Logroño, 26004, Spain

    J. M. Pérez-Izquierdo

Authors
  1. J. Mostovoy
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  2. J. M. Pérez-Izquierdo
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Additional information

The first author was partially supported by the CONACyT grant CO2-44100.

The second author acknowledges support from BFM2001-3239-C03-02 (MCYT) and ANGI2001/26 (Plan Riojano de I+D).

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Mostovoy, J., Pérez-Izquierdo, J.M. Dimension filtration on loops. Isr. J. Math. 158, 105–118 (2007). https://doi.org/10.1007/s11856-007-0005-y

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  • DOI: https://doi.org/10.1007/s11856-007-0005-y

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