2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167131A well-known Peterson's theorem says that the number of abelian ideals in a Borel subalgebra of a rank-$r$ finite dimensional simple Lie algebra is exactly $2^r$. In this paper, we determine the dimensional distribution of abelian ideals in a Borel subalgebra of finite dimensional simple Lie algebras, which is a refinement of the Peterson's theorem capturing more Lie algebra invariants.18 pagesQuantum Algebratext