Ideals in non-associative universal enveloping algebras of Lie
triple systems
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.
J.Mostovoy < jacob@matcuer.unam.mx >
J.M.Pérez-Izquierdo < jm.perez@dmc.unirioja.es >