E^n上一类酉算子的同构性质和应用

Isomorphism and Use of a Kind Unitary Operator

拓扑群O(n)对E^n的作用在拓扑学理论中是一个较为晦涩难懂的问题.文章通过定义了一个算子集合G,并证明了G与O(n)同构,由此又得出其它几个群之间的同构关系,从另一个角度阐述了拓扑群O(n)对E^n的作用,使该理论变得更加通俗直观.

To understand the effect of topological group O ( n) on En is a difficult problem. This paper difines a set of operator G ,proves that G and O(n) are isomorphism of group, and consequently illustrates that some is omorphism staying between the other groups. From a different perspective, the writer gives a new kind of explaination to the effect upon En by O ( n ) , thus helping people understand the theoretical idea.