对酉Clifford矩阵的补充说明(英文)

A supplement to the unitary Clifford matrix

俞祖国与王健在题为“高维M bius群的拓扑与共轭不变量”的文章中对酉Clifford矩阵进行了讨论 ,并得到了这样一个有趣的结论 :如果Clifford矩阵A =abcd 是一酉Clifford矩阵 ,则变换gA(x) =(ax+b) (cx +d) - 1 是弦度量空间 ( Rn,D)上的一个等距同胚 我们可以证明其逆命题也成立 另外 ,我们还证明了 2 维空间中酉矩阵与M bius变换的一些等价条件在n

YU Zu guo and WANG Jian in their paper“On the conjugate invariants and topology of Mbius group in higher dimensions” gave out some discussion about the unitary Clifford matrix,one of which is that if the Clifford matrix A=ab cd is a unitary Clifford matrix,then the transformation g A(x)=(ax+b)(cx+d) -1 is an isometry of the chordal metric space ( n,D) We prove the converse is also true.In addition,we discuss some other equivalent conditions for the unitary Clifford matrix,which are similar with those of 2 dimension.