| 总结: | <p>Let <em>g</em> be a Kac–Moody algebra and <em>b</em><sub>1</sub>,<em>b</em><sub>2</sub> be Borel subalgebras of opposite signs. The intersection <em>b</em>=<em>b</em><sub>1</sub>∩<em>b</em><sub>2</sub> is a finite-dimensional solvable subalgebra of <em>g</em>. We show that the nilpotency degree of [<em>b</em>,<em>b</em>] is bounded above by a constant depending only on <em>g</em>. This confirms a conjecture of Y. Billig and A. Pianzola [Y. Billig, A. Pianzola, Root strings with two consecutive real roots, Tohoku Math. J. (2) 47 (3) (1995) 391–403].</p>
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