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On Adjacency Preserving Maps

Published online by Cambridge University Press:  20 November 2018

R. Westwick
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In his paper [1] on homogeneous spaces W. L. Chow states that “ Any one-toone adjacency preserving transformation of the Grassmann space of all the [r] of Sn(0 < r < n— 1) onto itself is a transformation of the basic group of the space.” In the proof both the transformation and its inverse are assumed to be adjacency preserving. See also Dieudonne [2] p. 81.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 3 , 01 September 1974 , pp. 403 - 405
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Chow, W. L., On the Geometry of Algebraic Homogeneous Spaces. Ann. of Math. 50 (1949), 32-67.Google Scholar
2. Dieudonné, J., La Géométrie Des Groupes Classiques. 3rd edition, Springer-Verlag, Berlin Heidelberg New York (1971).Google Scholar