Adjacency preserving mappings of invariant subspaces of a null system

Huang, Wen-ling

doi:10.1090/S0002-9939-99-05456-8

Adjacency preserving mappings of invariant subspaces of a null system
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Proc. Amer. Math. Soc. 128 (2000), 2451-2455 Request permission

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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