We describe the set of lines of the three dimensional projective space over a not necessarily commutative field K as the projective line over the ring Mat(2,K) of 2x2-matrices with entries in K. Using this description, we investigate some families of lines such as reguli and spreads.
Blunck, A., Pianta, S., Lines in 3-space, <<MITTEILUNGEN DER MATHEMATISCHEN GESELLSCHAFT IN HAMBURG>>, 2008; (vol. 27): 189-202 [http://hdl.handle.net/10807/8031]
Lines in 3-space
Pianta, Silvia
2008
Abstract
We describe the set of lines of the three dimensional projective space over a not necessarily commutative field K as the projective line over the ring Mat(2,K) of 2x2-matrices with entries in K. Using this description, we investigate some families of lines such as reguli and spreads.
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