Nilpotent Sabinin algebras

  1. Mostovoy, J. 1
  2. Pérez-Izquierdo, J.M. 2
  3. Shestakov, I.P. 34
  1. 1 Instituto Politécnico Nacional

    Instituto Politécnico Nacional

    Ciudad de México, México

    GRID grid.418275.d

  2. 2 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

  3. 3 Universidade de São Paulo

    Universidade de São Paulo

    São Paulo, Brasil

    GRID grid.11899.38

  4. 4 Sobolev Institute of Mathematics

    Sobolev Institute of Mathematics

    Novosibirsk, Rusia

    GRID grid.426295.e

Journal of Algebra

ISSN: 0021-8693

Year of publication: 2014

Volume: 419

Pages: 95-123

Type: Article

Export: RIS
DOI: 10.1016/j.jalgebra.2014.07.015 SCOPUS: 2-s2.0-84906507964 WoS: 000342117200005 arXiv: 1312.2223 GOOGLE SCHOLAR lock_openOpen access editor
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In this paper we establish several basic properties of nilpotent Sabinin algebras. Namely, we show that nilpotent Sabinin algebras (1) can be integrated to produce nilpotent loops, (2) satisfy an analogue of the Ado theorem, (3) have nilpotent Lie envelopes. We also give a new set of axioms for Sabinin algebras. These axioms reflect the fact that a complementary subspace to a Lie subalgebra in a Lie algebra is a Sabinin algebra. Finally, we note that the non-associative version of the Jennings theorem produces a version of the Ado theorem for loops whose commutator-associator filtration is of finite length. © 2014.