There has been much work on strong and weak Lefschetz conditions for graded Artinian algebras A, especially those that are Gorenstein. A more general invariant of an algebra or finite A-module M we consider here is the set Jordan types elements maximal ideal

Let K be a field of characteristic zero. For integers n,D≥1, let Jn(D) the degree n component free Jordan algebra J(D) over D generators. A conjecture for character (in particular dimension) GL(D)-module is proposed. sl2J(D) Tits-Allison-Gao construction J(D). Two natural conjectures homology Lie are stated, and each them implies previous conjecture. The cyclicity structures, namely that symmet...