Projective representations i. projective lines over rings

By Andrea Blunck, Hans Havlicek. 2000

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We discuss representations of the projective line over a ringR with 1 in a projective space over some (not necessarily commutative) fieldK. Such a representation is based upon a (K, R)-bimoduleU. The points of the projective line overR are represented by certain subspaces of the projective space ℙ(K, U ×U) that are isomorphic to one of their complements. In particular, distant points go over to complementary subspaces, but in certain cases, also non-distant points may have complementary images.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/662d6ba0c4763e3f076de81ec719bbb2c477d4a6