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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Nilpotent Sabinin algebras

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Author(s):
Mostovoy, J. [1] ; Perez-Izquierdo, J. M. [2] ; Shestakov, I. P. [3, 4]
Total Authors: 3
Affiliation:
[1] IPN, CINVESTAV, Dept Matemat, Mexico City 07000, DF - Mexico
[2] Univ La Rioja, Dept Matemat & Comp, Logrono 26004 - Spain
[3] Sobolev Inst Math, Novosibirsk 630090 - Russia
[4] Univ Sao Paulo, Inst Matemat & Estat, BR-05311970 Sao Paulo - Brazil
Total Affiliations: 4
Document type: Journal article
Source: Journal of Algebra; v. 419, p. 95-123, DEC 1 2014.
Web of Science Citations: 2
Abstract

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. (C) 2014 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 10/50347-9 - Algebras, representations e applications
Grantee:Ivan Chestakov
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 12/22537-3 - Non-associative Lie theory
Grantee:Ivan Chestakov
Support Opportunities: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 12/21938-4 - Hopf algebras in non-associative Lie theory
Grantee:Ivan Chestakov
Support Opportunities: Research Grants - Visiting Researcher Grant - International