Nilpotent Sabinin algebras
- Mostovoy, J. 1
- Pérez-Izquierdo, J.M. 2
- Shestakov, I.P. 34
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1
Instituto Politécnico Nacional
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2
Universidad de La Rioja
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3
Universidade de São Paulo
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4
Sobolev Institute of Mathematics
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ISSN: 0021-8693
Année de publication: 2014
Volumen: 419
Pages: 95-123
Type: Article
D'autres publications dans: Journal of Algebra
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Résumé
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.