Cones and convex bodies with modular face lattices (Q2846858)
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scientific article; zbMATH DE number 6204368
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cones and convex bodies with modular face lattices |
scientific article; zbMATH DE number 6204368 |
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Cones and convex bodies with modular face lattices (English)
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3 September 2013
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convex body
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Hermitian matrix
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cones
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modular face lattices
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The authors study a class of convex bodies for which the lattices of their faces are modular. The main result of the paper isNEWLINENEWLINE{Theorem 3.} If \( C \) is a closed convex set in \( {\mathbb R}^n \) whose faces determine an affine space, then there is a face-preserving homeomorphism from \( C \) to a ``parabolic section'' of a cone of positive-semidefinite Hermitian matrices over \( {\mathbb R} \), \( {\mathbb C} \), or \( {\mathbb H} \), or \( C \) has dimension \(8\), \(14\) or \(26\).
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