TY - JOUR AU - Mostovoy, J. AU - Pérez-Izquierdo, J.M. AU - Shestakov, I.P. KW - Ado theorem KW - Baker-Campbell-Hausdorff formula KW - Commutator-associator filtration KW - Loop KW - Sabinin algebra T1 - Nilpotent Sabinin algebras LA - eng PY - 2014 SP - 95 EP - 123 T2 - Journal of Algebra SN - 0021-8693 VL - 419 AB - 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. DO - 10.1016/J.JALGEBRA.2014.07.015 UR - https://investigacion.unirioja.es/documentos/5bbc6977b750603269e81bbc DP - Dialnet - Portal de la Investigación ER -