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- W2261959398 abstract "It is well-known that the group of regular projective transf ormations of P 3 (R) is iso- morphic to the group of projective automorphisms of Klein's quadric M 4 2 ⊂ P 5 (R). We introduce the Clifford algebra Cl (3,3) constructed over the quadratic space R (3,3) and describe how points on Klein's quadric are embedded as null vectors, i.e., grade-1 elements squaring to zero. Furthermore, we discuss how geometric entities from Klein's model can be t ransferred to this homogeneous Clif- ford algebra model. Automorphic collineations of Klein's q uadric can be described by the action of the so called sandwich operator applied to vectors v ∈ V 1 V. Vectors correspond to null polarities in P 3 (R). We introduce a factorization algorithm. With the help of this algorithm we are able to factorize an arbitrary versor g ∈ Cl (3,3) into a set of non-commuting vectors vi ∈ V 1 V, i = 1,..., k, 1 ≤ k ≤ 6 corresponding to null polarities with g = v1...v k . Thus, we present a method to factorize every collineation in P 5 (R) that is induced by a projective transformation acting on P 3 (R) into a set of at most six involutoric automorphic collineations of Klein's quadric corresponding to null polarities re- spectively skew-symmetric 4× 4 matrices. Moreover, we give an outlook for Lie's sphere geo metry, i.e., the homogeneous Clifford algebra model constructed with the quadratic form corresponding to Lie's quadric L n+1 1 ⊂ P n+2 (R)." @default.
- W2261959398 created "2016-06-24" @default.
- W2261959398 creator A5027135788 @default.
- W2261959398 date "2014-06-02" @default.
- W2261959398 modified "2023-09-27" @default.
- W2261959398 title "NULL POLARITIES AS GENERATORS OF THE PROJECTIVE GROUP" @default.
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- W2261959398 hasPublicationYear "2014" @default.
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