6533b838fe1ef96bd12a5318
RESEARCH PRODUCT
Multiplicative Loops of Quasifields Having Complex Numbers as Kernel
Giovanni FalconeÁGota FigulaKarl Strambachsubject
Multiplicative loops of locally compact quasifields semifields sections in Lie groups translation planes automorphism groups.Applied Mathematics010102 general mathematicsMultiplicative functionDimension (graph theory)Lie groupField (mathematics)Translation (geometry)01 natural sciences010101 applied mathematicsCombinatoricsKernel (algebra)Mathematics (miscellaneous)Locally compact spaceSettore MAT/03 - Geometria0101 mathematicsComplex numberMathematicsdescription
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 $$Spin_3({\mathbb {R}})$$ . 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-05-31 |