Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Citations: Zbl 0528.30001; Zbl 0773.51001; Zbl 0295.50025; Zbl 0458.51020

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]