On the coadjoint representation of Z2-contractions of reductive Lie algebras

We study the coadjoint representation of contractions of reductive Lie algebras associated with symmetric decompositions. Let g=g0⊕g1 be a symmetric decomposition of a reductive Lie algebra g. Then the semi-direct product of g0 and the g0-module g1 is a contraction of g. We conjecture that these contractions have many properties in common with reductive Lie algebras. In particular, it is proved that in many cases the algebra of invariants is polynomial. We also discuss the so-called “codim-2 property” for coadjoint representations and its relationship with the structure of algebra of invariants.