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Cones and convex bodies with modular face lattices


Authors: Daniel Labardini-Fragoso, Max Neumann-Coto and Martha Takane
Journal: Proc. Amer. Math. Soc. 140 (2012), 4337-4350
MSC (2010): Primary 52A20, 06C05, 51A05, 15B48
DOI: https://doi.org/10.1090/S0002-9939-2012-11278-X
Published electronically: April 11, 2012
MathSciNet review: 2957224
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Daniel Labardini-Fragoso
Affiliation: Mathematisches Institut, Universität Bonn, D-53115 Bonn, Germany
Email: labardini@math.uni-bonn.de

Max Neumann-Coto
Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, Cuernavaca, México
Email: max@matcuer.unam.mx

Martha Takane
Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, Cuernavaca, México
Email: takane@matcuer.unam.mx

DOI: https://doi.org/10.1090/S0002-9939-2012-11278-X
Keywords: Convex, face lattice, modular, Hermitian matrix, projective space
Received by editor(s): February 20, 2009
Received by editor(s) in revised form: May 24, 2011
Published electronically: April 11, 2012
Additional Notes: Research partially supported by PAPIIT grants IN103508, IN101309 and a PASPA fellowship.
Dedicated: Dedicated to Claus M. Ringel on the occasion of his 65th birthday
Communicated by: Jim Haglund
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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