A uniform bound on the nilpotency degree of certain subalgebras of Kac-Moody algebras

Abstract

Let $\mathfrak{g}$ be a Kac-Moody algebra and ${\mathfrak{b}}_1,{\mathfrak{b}}_2$ be Borel subalgebras of opposite signs. The intersection $\mathfrak{b}={\mathfrak{b}}_1\cap {\mathfrak{b}}_2$ is a finite-dimensional solvable subalgebra of $\mathfrak{g}$. We show that the nilpotency degree of $[\mathfrak{b},\mathfrak{b}]$ is bounded from above by a constant depending only on $\mathfrak{g}$. This confirms a conjecture of Y. Billig and A. Pianzola \cite{BilligPia95}.

References in corpus (2)

• Isomorphisms of Kac-Moody groups which preserve bounded subgroups
• Conjugacy of 2-spherical subgroups of Coxeter groups and parallel walls

Cited by in corpus (3)

• On the structure of Kac-Moody algebras
• Construction of Commutator Blueprints
• Closed sets of real roots in Kac-Moody root systems