The length of PU(2,1) relative to special elliptic isometries with fixed parameter

2020/10/28 by Franco, Felipe A.
#51M10 #57S25 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2010.14677

Abstract

Generalizing the involution length of the complex hyperbolic plane, we obtain that the α-length of PU(2,1) is 4, that is, every element of PU(2,1) can be decomposed as the product of at most 4 special elliptic isometries with parameter α. We also describe the isometries that can be written as the product of 2 or 3 such special elliptic isometries.

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