非紧型嵌入黎曼对称空间的一个扩张定理及其泛性质的应用
An extension theorem for embedded Riemannian symmetric spaces of non-compact type and an application to their universal property
摘要：
已知在Loos意义下的抽象反射空间X中的测地线Y，在没有任何微分结构假设的情况下，正则地容许X的横截群的一个单参数子群的作用。在这篇文章中，我们证明了一个类似的结果，说明，如果X包含一个嵌入的双曲平面H，那么这将产生一个典型的作用，一个子群的横射群同构于PSL（2，R）的一个完美的中心扩张。这个结果可以进一步推广到嵌入X的任意非紧型黎曼对称空间，并且可以用来证明一个黎曼对称空间，更一般地说，代数单连通双球面Kac-Moody群G的Kac-Moody对称空间G/K满足一个类似于群G自身满足的泛性质的泛性质。
英文摘要：
It is known that a geodesic Y in an abstract reflection space X in the sense of Loos, without any assumption of differential structure, canonically admits an action of a 1-parameter subgroup of the group of transvections of X. In this article, we prove an analog of this result stating that, if X contains an embedded hyperbolic plane H, then this yields a canonical action of a subgroup of the transvection group of X isomorphic to a perfect central extension of PSL(2,R). This result can be further extended to arbitrary Riemannian symmetric spaces of non-compact type embedded in X and can be used to prove that a Riemannian symmetric space and, more generally, the Kac-Moody symmetric space G/K for an algebraically simply connected two-spherical Kac-Moody group G satisfies a universal property similar to the universal property that the group G satisfies itself.
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