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Traces, Cross-Ratios and 2-Generator Subgroups of $\SU(2,1)$ |
Canad. J. Math. 61(2009), 1407-1436
Published:2009-12-01
Printed: Dec 2009
Printed: Dec 2009
- Pierre Will
Abstract
In this work, we investigate how to decompose a pair $(A,B)$ of
loxodromic isometries of the complex hyperbolic plane $\mathbf H^{2}_{\mathbb C}$ under
the form $A=I_1I_2$ and $B=I_3I_2$, where the $I_k$'s are
involutions. The main result is a decomposability criterion, which
is expressed in terms of traces of elements of the group $\langle
A,B\rangle$.
| MSC Classifications: |
14L24 - Geometric invariant theory [See also 13A50] 22E40 - Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 32M15 - Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15] 51M10 - Hyperbolic and elliptic geometries (general) and generalizations |