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

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

2006-12-17

arxiv.org/abs/math/0612482v1

J. Algebra 317 (2007), pp.867--876

Mathematics

Rings and Algebras

Scientific paper

10.1016/j.jalgebra.2007.04.002

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}.

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