Octonions, triality, the exceptional Lie algebra F4 and polar actions on the Cayley hyperbolic plane

DOI10.1142/S0129167X20500512zbMath1461.53042arXiv1802.08075OpenAlexW3010791855WikidataQ115246503 ScholiaQ115246503MaRDI QIDQ5853654

Andreas Kollross

Publication date: 11 March 2021

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.08075

zbMATH Keywords

octonionsexceptional Lie algebrapolar actionCayley hyperbolic plane

Mathematics Subject Classification ID

Differential geometry of symmetric spaces (53C35) Noncompact Lie groups of transformations (57S20) Nonassociative division algebras (17A35)

Related Items (1)

Polar actions on Damek-Ricci spaces

Cites Work

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• Some remarks on polar actions
• Polar foliations of symmetric spaces
• Polar actions with a fixed point
• Singular Riemannian foliations and isoparametric submanifolds
• Low cohomogeneity and polar actions on exceptional compact Lie groups
• A geometric construction of the exceptional Lie algebras \(F_4\) and \(E_8\)
• Oktaven, Ausnahmegruppen und Oktavengeometrie
• Certain isoparametric families of hypersurfaces in symmetric spaces
• Homogeneous hypersurfaces in hyperbolic spaces
• Generalized Heisenberg groups and Damek-Ricci harmonic spaces
• Homogeneous spaces with polar isotropy
• Polar actions on rank-one symmetric spaces.
• Polar actions on complex hyperbolic spaces
• Homogeneous codimension one foliations on noncompact symmetric spaces.
• Compact transformation groups on rational cohomology Cayley projective planes
• Cohomogeneity one actions on noncompact symmetric spaces with a totally geodesic singular orbit
• Invariant four-forms and symmetric pairs
• On homogeneous real hypersurfaces in a complex projective space
• Homogeneous structures on real and complex hyperbolic spaces
• Polar actions on symmetric spaces
• Minimal submanifolds of low cohomogeneity
• On subgroups of the noncompact real exceptional Lie group \(F_4^*\)
• Elliptic spaces in Grassmann manifolds
• Cohomogeneity one actions on hyperbolic spaces
• A classification of hyperpolar and cohomogeneity one actions
• Polar Actions on Symmetric Spaces
• Duality of symmetric spaces and polar actions
• The maximal subgroups of the classical groups
• Cohomogeneity one actions on noncompact symmetric spaces of rank one
• Polar Coordinates Induced by Actions of Compact Lie Groups
• A General Theory of Canonical Forms
• Isoparametric Submanifolds of Hyperbolic Spaces
• The octonions
• Polar actions on symmetric spaces of higher rank
• Inclusion relations among transitive compact transformation groups
• The Exceptional Simple Lie Algebras F ₄ and E ₆

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