  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.
