An Envelope for Malcev Algebras

  1. Pérez-Izquierdo, J.M. 1
  2. Shestakov, I.P. 23
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidade de São Paulo
    info

    Universidade de São Paulo

    São Paulo, Brasil

    ROR https://ror.org/036rp1748

  3. 3 Sobolev Institute of Mathematics
    info

    Sobolev Institute of Mathematics

    Novosibirsk, Rusia

    ROR https://ror.org/00shc0s02

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Revista:
Journal of Algebra

ISSN: 0021-8693

Año de publicación: 2004

Volumen: 272

Número: 1

Páginas: 379-393

Tipo: Artículo

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DOI: 10.1016/S0021-8693(03)00389-2 SCOPUS: 2-s2.0-1642519720 WoS: WOS:000188064100015 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Journal of Algebra

Repositorio institucional: lock_openAcceso abierto Editor

Resumen

We prove that for every Malcev algebra M there exist an algebra U(M) and a monomorphism ι:M → U(M)- of M into the commutator algebra U(M)- such that the image of M lies into the alternative center of U(M), and U(M) is a universal object with respect to such homomorphisms. The algebra U(M), in general, is not alternative, but it has a basis of Poincaré-Birkhoff-Witt type over M and inherits some good properties of universal enveloping algebras of Lie algebras. In particular, the elements of M can be characterized as the primitive elements of the algebra U(M) with respect to the diagonal homomorphism Δ:U(M) → U(M) ⊗ U(M). An extension of Ado-Iwasawa theorem to Malcev algebras is also proved. © 2004 Published by Elsevier Inc.