Hyperplane section \({\mathbb {O}\mathbb {P}}^2_0\) of the complex Cayley plane as the homogeneous space \({\text F}_4/{\text P}_4\). (Q2897373)
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scientific article; zbMATH DE number 6054241
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hyperplane section \({\mathbb {O}\mathbb {P}}^2_0\) of the complex Cayley plane as the homogeneous space \({\text F}_4/{\text P}_4\). |
scientific article; zbMATH DE number 6054241 |
Statements
10 July 2012
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Cayley plane
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octonionic contact structure
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twistor fibration
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parabolic geometry
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Severi variety
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hyperplane section
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exceptional geometry
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math.AG
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math.DG
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Hyperplane section \({\mathbb {O}\mathbb {P}}^2_0\) of the complex Cayley plane as the homogeneous space \({\text F}_4/{\text P}_4\). (English)
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The authors present a transitive action of the exceptional complex Lie group \(F_4\) on the hyperplane section of the complex Cayley plane \({\mathbb {O}\mathbb {P}}^2\). Clifford algebras, spin groups and the representation theory are used.
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