Search results for "Sections in Lie group"

showing 2 items of 2 documents

Multiplicative loops of 2-dimensional topological quasifields

2015

We determine the algebraic structure of the multiplicative loops for locally compact $2$-dimensional topological connected quasifields. In particular, our attention turns to multiplicative loops which have either a normal subloop of positive dimension or which contain a $1$-dimensional compact subgroup. In the last section we determine explicitly the quasifields which coordinatize locally compact translation planes of dimension $4$ admitting an at least $7$-dimensional Lie group as collineation group.

CollineationAlgebraic structureDimension (graph theory)Topology01 natural sciencesSection (fiber bundle)TermészettudományokFOS: MathematicsCollineation groupLocally compact space0101 mathematicsMatematika- és számítástudományokMathematicsAlgebra and Number TheoryGroup (mathematics)010102 general mathematicsMultiplicative function20N05 22A30 12K99 51A40 57M60Lie groupMathematics - Rings and AlgebrasSections in Lie group010101 applied mathematicsTranslation planes and speadsMultiplicative loops of locally compact quasifieldRings and Algebras (math.RA)Settore MAT/03 - Geometria
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Multiplicative Loops of Quasifields Having Complex Numbers as Kernel

2017

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.

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 numberMathematics
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