Unitals over composition algebras
-
Norbert Knarr
and
Markus Stroppel
Abstract.
We consider polar unitals in projective planes over composition algebras. We prove that the little projective group of such a unital is contained in the centralizer of the polarity defining the unital. This yields information about the full automorphism group of the unital; it is contained in the automorphism group of the normal subgroup generated by all translations of the unital. Over suitable ground fields (such as the real numbers) we obtain a complete description of the automorphism group of the unital in the sense that it coincides with the centralizer of the polarity. The action of a nilpotent regular normal subgroup is used to establish isomorphisms between unitals in spaces of different dimensions, and over different fields.
© 2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Smooth global solutions for the two-dimensional Euler Poisson system
- Primitive ideals in quantum Schubert cells: Dimension of the strata
- Group valued null sequences and metrizable non-Mackey groups
- The splitting relation for Fréchet spaces over non-archimedean fields
- Bloch–Kato pro-p groups and locally powerful groups
- On Lp resolvent estimates for Laplace–Beltrami operators on compact manifolds
- The Ext functor and self-sums
- Auslander–Reiten translations in monomorphism categories
- An elementary proof of the vanishing of the second cohomology of the Witt and Virasoro algebra with values in the adjoint module
- Unitals over composition algebras
- Separation of bi-harmonic differential operators on Riemannian manifolds
Articles in the same Issue
- Frontmatter
- Smooth global solutions for the two-dimensional Euler Poisson system
- Primitive ideals in quantum Schubert cells: Dimension of the strata
- Group valued null sequences and metrizable non-Mackey groups
- The splitting relation for Fréchet spaces over non-archimedean fields
- Bloch–Kato pro-p groups and locally powerful groups
- On Lp resolvent estimates for Laplace–Beltrami operators on compact manifolds
- The Ext functor and self-sums
- Auslander–Reiten translations in monomorphism categories
- An elementary proof of the vanishing of the second cohomology of the Witt and Virasoro algebra with values in the adjoint module
- Unitals over composition algebras
- Separation of bi-harmonic differential operators on Riemannian manifolds
