a note on 2-plectic vector spaces

Among the 2-plectic structures on vector spaces, the canon-ical ones and the 2-plectic structures induced by the killing form on semisimple lie algebras are more interesting. in this note, we show that the group of linear preservers of the canonical 2-plectic structure is non-compact and disconnected and its dimension is computed. also, we show that the group of automorphisms of a compact semisimple lie algebra preserving its 2-plectic structure, is compact. furthermore, it is shown that the 2-plectic structure on a semisimple lie algebra g is canonical if and only if it has an abelian lie subalgebra whose dimension satisfies in a special condition. as a consequence, we conclude that the 2-plectic structures induced by the killing form on some important classical lie algebras are not canonical.