3-Graded Lie algebras with Jordan finiteness conditions
A notion of socle is introduced for 3-graded Lie algebras
(over a ring of scalars containing 1/6) whose associated Jordan pairs
are non-degenerate. The socle turns out to be a 3-graded ideal and is
the sum of some minimal 3-graded inner ideals, each of which being a
central extension of the TKK-algebra of a division Jordan pair.
Non-degenerate 3-graded Lie algebras having a large socle are
essentially determined by TKK-algebras of simple Jordan pairs with
minimal inner ideals and their derivation algebras, which are also
3-graded.
(This paper has appeared in Comm. Algebra 32 (2004), no.
10, 3807--3824)
A. Fernández López < emalfer@agt.cie.uma.es >
E. García < egarciag@mat.ucm.es >
M. Gómez Lozano < magomez@agt.cie.uma.es >