Oktaven, Ausnahmegruppen und Oktavengeometrie

  title={Oktaven, Ausnahmegruppen und Oktavengeometrie},
  author={Hans Freudenthal},
  journal={Geometriae Dedicata},
The real quadrangle of typeE6
Based on the first author's diploma thesis (11) we use the theories of Lie groups and of Tits buildings in order to describe a Veronese embedding of the real quadrangle of type E6, i.e., the C2Expand
Octonions, triality, the exceptional Lie algebra F4 and polar actions on the Cayley hyperbolic plane
Using octonions and the triality property of Spin(8), we find explicit formulae for the Lie brackets of the exceptional simple real Lie algebras $\mathfrak{f}_4$ and $\mathfrak{f}^*_4$, i.e. the LieExpand
The real quadrangle of type E6
We give a geometric interpretation of the building associated to the real Lie group E_6(-14) in terms of its 54-dimensional module.
Developments in finite Phan theory
This is a final report on finite Phan theory, a project that has been concerned with a revision and generalisation of Phan's presentation results of twisted Chevalley groups over finite fields withExpand
Property (RD) for Cocompact Lattices in a Finite Product of Rank One Lie Groups with Some Rank Two Lie Groups
We apply V. Lafforgue′s techniques to establish property (RD) for cocompact lattices in a finite product of rank one Lie groups with Lie groups whose restricted root system is of type A2.
Arithmetic and topology of classical structures associated to plane quartics
We consider moduli spaces of plane quartics marked with various structures such as Cayley octads, Aronhold heptads, Steiner complexes and Göpel subsets and determine their cohomology. This answers aExpand
M-theory, black holes and cosmology
  • R. Kallosh
  • Physics, Mathematics
  • Proceedings of the Royal Society A
  • 2021
A relation between STU black hole entropy, the Cayley hyperdeterminant, the Bhargava cube and a three-qubit Alice–Bob–Charlie triality symmetry is described and puzzling relations between the fermion mass eigenvalues in these cosmological models are shown. Expand
Halving spaces and lower bounds in real enumerative geometry
We develop the theory of halving spaces to obtain lower bounds in real enumerative geometry. Halving spaces are topological spaces with an action of a Lie group $\Gamma$ with additional cohomologicalExpand
Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic form
There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of theExpand
On Lie algebras of type F4 and Chevalley groups F4(K), E6(K), and 2E6(K) for fields K of characteristic two
Abstract In this article, we give an elementary and self-contained approach to construct the Lie algebras of type over an arbitrary field K of characteristic two. The Lie algebras are represented asExpand


The Exceptional Simple Lie Algebras F(4) and E(6).
  • C. Chevalley, R. D. Schafer
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1950
Les groupes réels simples, finis et continus
© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1914, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.Expand