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Multiplicative Loops of Quasifields Having Complex Numbers as Kernel

  • Autori: Falcone, G.; Figula, Á.; Strambach, K.
  • Anno di pubblicazione: 2017
  • Tipologia: Articolo in rivista (Articolo in rivista)
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We determine the multiplicative loops of locally compact connected 4-dimensional quasifields Q having the field of complex numbers as their kernel. In particular, we turn our attention to multiplicative loops which have either a normal subloop of dimension one or which contain a subgroup isomorphic to Spin3(R). Although the 4-dimensional semifields Q are known, their multiplicative loops have interesting Lie groups generated by left or right translations. We determine explicitly the quasifields Q which coordinatize locally compact translation planes of dimension 8 admitting an at least 16-dimensional Lie group as automorphism group.