Ideals in non-associative universal enveloping algebras of Lie triple systems

  1. Mostovoy, J. 1
  2. Pérez-Izquierdo, J.M. 2
  1. 1 Instituto Politécnico Nacional
    info

    Instituto Politécnico Nacional

    Ciudad de México, México

    ROR https://ror.org/059sp8j34

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Forum Mathematicum

ISSN: 0933-7741

Año de publicación: 2010

Volumen: 22

Número: 1

Páginas: 1-20

Tipo: Artículo

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DOI: 10.1515/FORUM.2010.001 SCOPUS: 2-s2.0-77950254592 WoS: WOS:000275683100001 GOOGLE SCHOLAR

Otras publicaciones en: Forum Mathematicum

Proyectos relacionados

Álgebras, triples y lazos relacionados con Geometría y Supersimetría

2007/00082/001

Resumen

The notion of a non-associative universal enveloping algebra for a Lie triple system arises when Lie triple systems are considered as Bol algebras (more generally, Sabinin algebras). In this paper a new construction for these universal enveloping algebras is given, and their properties are studied. It is shown that universal enveloping algebras of Lie triple systems have surprisingly few ideals. It is conjectured, and the conjecture is verified on several examples, that the only proper ideal of the universal enveloping algebra of a simple Lie triple system is the augmentation ideal. © 2010 de Gruyter.