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 -