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

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

2005-06-09

arxiv.org/abs/math/0506179v1

Mathematics

Rings and Algebras

14 pages

Scientific paper

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.

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