Adjacency preserving mappings of invariant subspaces of a null system
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Abstract:
In the space $I_r$ of invariant $r$-dimensional subspaces of a null system in $(2r+1)$-dimensional projective space, W.L. Chow characterized the basic group of transformations as all the bijections $\varphi :I_r\to I_r$, for which both $\varphi$ and $\varphi ^{-1}$ preserve adjacency. In the present paper we show that the two conditions $\varphi :I_r\to I_r$ is a surjection and $\varphi$ preserves adjacency are sufficient to characterize the basic group. At the end of this paper we give an application to Lie geometry.References
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Additional Information
- Wen-ling Huang
- Affiliation: Mathematisches Seminar, Universität Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany
- Email: huang@math.uni-hamburg.de
- Received by editor(s): September 25, 1998
- Published electronically: November 29, 1999
- Communicated by: Christopher Croke
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2451-2455
- MSC (1991): Primary 51A50; Secondary 51B25
- DOI: https://doi.org/10.1090/S0002-9939-99-05456-8
- MathSciNet review: 1690993