Kollineationen von Translationsstrukturen |
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Authors: | Werner Seier |
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Institution: | (1) Mathematisches Seminar der UniversitÄt, Rothenbaumchaussee 67/69, 2 Hamburg 13 |
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Abstract: | Translationstructures are generalized affine spaces. They can be described algebraically by partitions of groups. For desarguesian affine spaces the group is a vectorspace and the partition is the set of all onedimensional subspaces. In this case each collineation fixing 0 is a regular semilinear mapping, i.e. an automorphism of the vectorspace. In the general case it is a mapping called equivalence. Each equivalence of a partition is an automorphism iff the set of translations of the group is a normal subgroup of the collineationgroup. The translations form a normal subgroup, if the group is finite or abelian. We prove some theorems for the infinite non abelian case. |
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