### Abstract

We determine the multiplicative loops of locally compact connected4-dimensional quasifields Q having the field of complex numbersas their kernel. In particular, we turn our attention to multiplicative loopswhich have either a normal subloop of dimension one or which contain asubgroup isomorphic to Spin3(R). Although the 4-dimensional semifieldsQ are known, their multiplicative loops have interesting Lie groups generatedby left or right translations. We determine explicitly the quasifieldsQ which coordinatize locally compact translation planes of dimension 8admitting an at least 16-dimensional Lie group as automorphism group.

Lingua originale | English |
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Numero di pagine | 28 |

Rivista | Results in Mathematics |

Stato di pubblicazione | Published - 2017 |

### All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)
- Applied Mathematics

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## Cita questo

Falcone, G., Falcone, G., Strambach, K., & Figula, Á. (2017). Multiplicative Loops of Quasifields Having Complex Numbers as Kernel.

*Results in Mathematics*.