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Conjugacy invariants of Sl(2,). (English) Zbl 1048.15015

The author determines conjugacy invariants of Sl(2,), where denotes the real quaternions. This leads then to a classification of projectivities, i.e. the elements of PSl(2,).

Reviewer’s remarks: On page 26 the classification of (direct) Möbius transformations on the complex projective line is cited incorrectly from [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 L. Gyarmathi [Publ. Math. 21, 233–248 (1974; Zbl 0295.50025) and ibid. 27, 93–106 (1980; Zbl 0458.51020)].

MSC:
15A33Matrices over special rings
51M10Hyperbolic and elliptic geometries (general) and generalizations