Kac-Moody代数中某些子代数幂零度的一致界
A uniform bound on the nilpotency degree of certain subalgebras of Kac-Moody algebras
摘要：
设$\mathfrak{g}$是Kac-Moody代数，$\mathfrak{b}_1, \mathfrak{b}_2$是符号相反的Borel子代数.交$\mathfrak{b} = \mathfrak{b}_1 \cap \mathfrak{b}_2$是$\mathfrak{g}$的有限维可解子代数。我们证明了$[\mathfrak{b}, \mathfrak{b}]$的幂零度是由一个只依赖于$\mathfrak{g}$的常数从上到下有界的。这证实了Y. Billig和A. Pianzola \cite{BilligPia95}。
英文摘要：
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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