Cones and convex bodies with modular face lattices

Labardini-Fragoso, Daniel; Neumann-Coto, Max; Takane, Martha

doi:10.1090/S0002-9939-2012-11278-X

Cones and convex bodies with modular face lattices
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by Daniel Labardini-Fragoso, Max Neumann-Coto and Martha Takane PDF

Proc. Amer. Math. Soc. 140 (2012), 4337-4350 Request permission

Abstract:

If a convex body $C$ in $\mathbb {R}^{n}$ has modular and irreducible face lattice and $C$ is not strictly convex, there is a face-preserving homeomorphism from $C$ to a set of positive-semidefinite Hermitian matrices of trace 1 over $\mathbb {R}$, $\mathbb {C}$ or $\mathbb {H}$, or $C$ has dimension 8, 14 or 26.

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