Geometrical characterization of semilinear isomorphisms of vector spaces and semilinear homeomorphisms of normed spaces

2013/04/05 by Mark Pankov, Pankov, Mark
Mathematics · #46B03 #51A10 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.CO #math.GR #math.RT #msc:46B03 #msc:51A10

paper · pdf · doi:10.48550/arxiv.1304.1626

arxiv created 2013/09/25 · arxiv updated 2013/09/26

Abstract

Let V and V' be vector spaces over division rings (possible infinite-dimensional) and let \mathcal P(V) and \mathcal P(V') be the associated projective spaces. We say that f:\mathcal P(V)→ \mathcal P(V') is a PGL-\it mapping if for every h∈ \rm PGL(V) there exists h'∈ \rm PGL(V') such that fh=h'f. We show that for every PGL-bijection the inverse mapping is a semicollineation. Also, we obtain an analogue of this result for the projective spaces associated to normed spaces.

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