有界生成与不能作用于直线上的格
Bounded generation and lattices that cannot act on the line
摘要：
设D是连通的半单李群G中的不可约格，G具有有限中心.设G的实秩至少为2，G/D不是紧的，并且G有多个非紧单因子。我们证明了D在实直线上没有方向保持作用。(In代数项，这意味着D不是右可序的。）在G的单因子不与SL（2，R）同构的附加假设下，应用E.Ghys的定理得出结论：D在圆上的任何方向保持作用必须通过D的有限阿贝尔商分解。这个证明依赖于D.Carter、G.Keller和E.Paige证明的事实，即SL（2，A）是由幂零元有界生成的，只要A是一个有无穷多个单位的整数环。如果SL（3，R）和SL（3，C）中的所有非余紧格都是由幂幺子虚有界生成的，则G有多个非紧单因子的假设可以消除。
英文摘要：
Let D be an irreducible lattice in a connected, semisimple Lie group G with finite center. Assume that the real rank of G is at least two, that G/D is not compact, and that G has more than one noncompact simple factor. We show that D has no orientation-preserving actions on the real line. (In algebraic terms, this means that D is not right orderable.) Under the additional assumption that no simple factor of G is isogenous to SL(2,R), applying a theorem of E.Ghys yields the conclusion that any orientation-preserving action of D on the circle must factor through a finite, abelian quotient of D. The proof relies on the fact, proved by D.Carter, G.Keller, and E.Paige, that SL(2,A) is boundedly generated by unipotents whenever A is a ring of integers with infinitely many units. The assumption that G has more than one noncompact simple factor can be eliminated if all noncocompact lattices in SL(3,R) and SL(3,C) are virtually boundedly generated by unipotents.
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