两个椭圆四元数mÖbius变换的自由积

Pub Date : 2017-04-01 DOI:10.18910/61891

W. Cao

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引用次数: 0

摘要

想那f和g是二号elliptic quaternionic M¨obius transformations of命令M和n respectively。如果《ﬁ之间距离hyperbolicδ(f, g) x (f)条和cosh xﬁ萨蒂(g)ﬁ冰δ(f, g)≥因为ππn + 1,因为sinπm辛πn,然后《集团(cid 4: 3) f, g (cid)是discrete non-elementary和同构免费广告(cid》:3)f (cid 3: 4)∗(cid) g (cid: 4)。

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FREE PRODUCT OF TWO ELLIPTIC QUATERNIONIC MÖBIUS TRANSFORMATIONS

Suppose that f and g are two elliptic quaternionic M¨obius transformations of orders m and n respectively. If the hyperbolic distance δ ( f , g ) between ﬁx( f ) and ﬁx( g ) satisﬁes cosh δ ( f , g ) ≥ cos π m cos π n + 1 sin π m sin π n , then the group (cid:3) f , g (cid:4) is discrete non-elementary and isomorphic to the free product (cid:3) f (cid:4) ∗ (cid:3) g (cid:4) .

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