Ideals in Non-associative Universal Enveloping Algebras of Lie Triple Systems
نویسندگان
چکیده
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.
منابع مشابه
Right ideals in non–associative universal enveloping algebras of Lie triple systems
We prove that the only proper right ideal of the universal enveloping algebra of a finite–dimensional central simple Lie triple system over a field of characteristic zero is its augmentation ideal.
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