Division algebras与建筑物上群作用的传递性
Division algebras and transitivity of group actions on buildings
摘要：
设D是一个中心为F且度d>2的除代数.设K| F是任何分裂场。我们分析了D^ \times和SL_1（D）对可能与GL_d（K）和SL_d（K）相关联的球面和仿射建筑物的作用，特别证明了它从来不是强传递的.在仿射的情况下，我们发现的例子，行动仍然是外尔传递。这扩展了Abramenko和Brown关于d=2情形的结果，其中强传递性实际上是可能的。我们的方法产生了一些明确的结构，我们发现，对于d>2的失败的行动是强传递的是相当戏剧性的。
英文摘要：
Let D be a division algebra with center F and degree d>2. Let K|F be any splitting field. We analyze the action of D^\times and SL_1(D) on the spherical and affine buildings that may be associated to GL_d(K) and SL_d(K), and in particular show it is never strongly transitive. In the affine case we find examples where the action is nonetheless Weyl transitive. This extends results of Abramenko and Brown concerning the d=2 case, where strong transitivity is in fact possible. Our approach produces some explicit constructions, and we find that for d>2 the failure of the action to be strongly transitive is quite dramatic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
