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Products of Elations and Harmonic Homologies

Published online by Cambridge University Press:  20 November 2018

Erich W. Ellers
Erich W. Ellers*
Affiliation:
Department of Mathematics, University of Toronto Toronto, Ontario M5S 1A1, Canada
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Abstract

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The projective special linear group PSL(V) is generated by dations. Among all factorizations of p ∈ PSL(V) into dations there will be one (or more) with the least number of factors. We determine this number, i.e. we solve the length problem for the projective special linear group. We solve a similar problem for the projective unimodular group which is generated by harmonic homologies. The projective special linear group and the projective unimodular group are the most important special cases of projective hyperreflection groups. We also solve the length problem for the general case.

Keywords

51N3020H20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 4 , 01 December 1985 , pp. 397 - 400
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Artin, E., Geometric Algebra, Interscience Publishers, New York, 1957.Google Scholar
2. Bachmann, F., Aufbau der Géométrie aus dem Spiegelungsbegriff (2nd ed.). Springer-Verlag, New York-Heidelberg-Berlin, 1973.Google Scholar
3. Ellers, E.W., Decomposition of Equiajfinitie s into Reflections, Geom. Dedicata 6 (1977), pp. 297–304.Google Scholar
4. Ellers, E.W., Projective Collineations as Products of Homologies, Elations, and Projective Reflections, Aequ. Math. 25 (1982), pp. 103–114.Google Scholar
5. Ellers, E.W., Products of Axial Affinities and Products of Central Collineations, The Geometric Vein, Springer-Verlag, New York, 1982, pp. 465–470.Google Scholar
6. Scherk, P., On the Decomposition of Orthogonalities into Symmetries, Proc Amer. Math. Soc. 1 (1950), pp. 481–491.Google Scholar