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Quasi-simple Lie groups as multiplication groups of topological loops
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Ágota Figula
Published/Copyright:
July 3, 2015
Abstract
We prove that among the quasi-simple Lie groups only the group SL4(ℝ) occurs as the multiplication group of 3-dimensional connected topological loops L. These loops L are homeomorphic to the sphere S3. Moreover, there does not exist any connected topological loop having an at most 8-dimensional quasi-simple Lie groups as its multiplication group.
Keywords : Multiplication group of topological loops; topological transformation groups; sections in Lie groups; quasi-simple Lie groups
Received: 2013-9-9
Revised: 2013-9-12
Published Online: 2015-7-3
Published in Print: 2015-7-1
© 2015 by Walter de Gruyter Berlin/Boston
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- A natural extension of the Young partition lattice
- Pencils of small degree on curves on unnodal Enriques surfaces
- Michael’s Selection Theorem in a semilinear context
- Quasi-simple Lie groups as multiplication groups of topological loops
- Some spectral results on Kakeya sets
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Keywords for this article
Multiplication group of topological loops;
topological transformation groups;
sections in Lie groups;
quasi-simple Lie groups
Articles in the same Issue
- Frontmatter
- A natural extension of the Young partition lattice
- Pencils of small degree on curves on unnodal Enriques surfaces
- Michael’s Selection Theorem in a semilinear context
- Quasi-simple Lie groups as multiplication groups of topological loops
- Some spectral results on Kakeya sets
- Projective normality and the generation of the ideal of an Enriques surface
- Topological contact dynamics I: symplectization and applications of the energy-capacity inequality
- Torsion-free G*2(2)-structures with full holonomy on nilmanifolds
