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Geometry of kinematicK-loops

Abstract

AK-loop is called kinematic, if a further condition (K7) is valid. Such a loop (L, ⊕) can be provided in a natural way with a left and right structureL andG such that (L,L) and (L,G) become incidence (linear) spaces. For (L,L) andtL, each left translationt +:LL;xbx is a collineation and (L,G) can be turned in an incidence space with parallelism (L,G, ‖). Examples of kinematicK-loops are given for which the corresponding automorphisms δa,b are either the identity or fixed point free.

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Kolb, E., Kreuzer, A. Geometry of kinematicK-loops. Abh.Math.Semin.Univ.Hambg. 65, 189 (1995). https://doi.org/10.1007/BF02953325

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Keywords

  • Maximal Ideal
  • Jacobson Radical
  • Holomorphic Automorphism
  • Power Series Ring
  • Complex Disc