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arXiv · 1501.05635

Dimension-raising Homomorphisms between Lattices of Convex Bodies

Luisa Allgaier·Heinz Weisshaupt
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Abstract

We settle the first unsolved case of a problem of P. M. Gruber, asked by him in 1991, namely, to investigate the homomorphisms from the lattice of convex bodies of ${\mathbb{E}}^c$ to the lattice of convex bodies of ${\mathbb{E}}^d$ for $c<d$. We completely describe these homomorphisms for the case $d=c+1$, for $c \ge 3$. The obtained result is then applied to characterize anti-homomorphisms and homomorphisms from lattices of convex bodies to lattices of convex functions.

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Luisa Allgaier, Heinz Weisshaupt. 2015-01-22. Dimension-raising Homomorphisms between Lattices of Convex Bodies. https://arxiv.org/abs/1501.05635

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