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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Adjacency preserving mappings
of invariant subspaces of a null system


Author: Wen-ling Huang
Journal: Proc. Amer. Math. Soc. 128 (2000), 2451-2455
MSC (1991): Primary 51A50; Secondary 51B25
Published electronically: November 29, 1999
MathSciNet review: 1690993
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05456-8
PII: S 0002-9939(99)05456-8
Keywords: Null system, adjacency preserving mappings, symmetric matrices, Lie transformations
Received by editor(s): September 25, 1998
Published electronically: November 29, 1999
Communicated by: Christopher Croke
Article copyright: © Copyright 2000 American Mathematical Society