Abelian ideals with given dimension in Borel subalgebras

Details Abelian ideals with given dimension in Borel subalgebras Abelian ideals with given dimension in Borel subalgebras

2008-08-15

arxiv.org/abs/0808.2086v1

Mathematics

Quantum Algebra

18 pages

Scientific paper

A 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.

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