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Zbl 1048.15015
Foreman, B.
Conjugacy invariants of $Sl(2,\Bbb H)$.
(English)
[J] Linear Algebra Appl. 381, 25-35 (2004). ISSN 0024-3795

The author determines conjugacy invariants of Sl$(2,{\Bbb H})$, where ${\Bbb H}$ denotes the real quaternions. This leads then to a classification of projectivities, i.e. the elements of PSl$(2,{\Bbb H})$. \par Reviewer's remarks: On page 26 the classification of (direct) Möbius transformations on the complex projective line is cited incorrectly from [{\it A. F. Beardon}, The geometry of discrete groups (1983; Zbl 0528.30001), p.\ 67]: the strictly loxodromic transformations are missing, and the identity has to be ruled out. By a completely different approach, a classification not only of the projectivities but also of the anti-projectivities on the quaterionic projective line was given by the reviewer [Publ. Math. 40, No. 3--4, 219--227 (1992; Zbl 0773.51001)] based upon two papers of {\it L. Gyarmathi} [Publ. Math. 21, 233--248 (1974; Zbl 0295.50025) and ibid. 27, 93--106 (1980; Zbl 0458.51020)].
[Hans Havlicek (Wien)]
MSC 2000:
*15A33 Matrices over special rings
51M10 Hyperbolic and elliptic geometries (general) and generalizations

Keywords: Möbius transformation; hyperbolic geometry; quaternions; quaternionic matrix algebra

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