The inner ideals of the classical Lie algebras, related
gradings and Jordan pairs
The inner ideals of the simple finite dimensional Lie
algebras over an algebraically closed field of characteristic 0 are
classified up to conjugation by automorphisms of the Lie algebra, and
up to Jordan isomorphisms of their corresponding subquotients (any
proper inner ideal of a classical Lie algebra is abelian and
therefore it has a subquotient which is a simple Jordan pair). While
the description of the inner ideals of the Lie algebras of types
An, Bn, Cn and Dn can be
obtained from the Lie inner ideal structure of the simple Artinian
rings and simple Artinian rings with involution, the description of
the inner ideals of the exceptional Lie algebras (types
G2, F4, E6, E7 and
E8) remained open. The method we use here to classify
inner ideals is based on the relationship between abelian inner
ideals and Z-gradings, obtained in a recent paper of the three
last-named authors with E. Neher. This reduces the question to deal
with root systems.
(This paper has now appeared under the title "The inner ideals of the simple
finite dimensional Lie algebras" in J. Lie Theory 22 (2012), No. 4,
907--929)
C. Draper < cdf@uma.es >
A. Fernández López < emalfer@agt.cie.uma.es >
E. García < esther.garcia@urjc.es >
M. Gómez Lozano < magomez@agt.cie.uma.es >