Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 49, No. 2, pp. 541-547 (2008)
The endomorphisms of the lattice of closed convex cones
Rolf SchneiderMathematisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg i. Br., Germany, e-mail: email@example.com
Abstract: The set of closed convex cones in $\R^d$ ($d\ge 3$), with the operations of intersection and closed sum, is a lattice. We determine all endomorphisms of this lattice. As a consequence, we obtain a characterization of the duality of convex cones.
Keywords: lattice of convex cones, lattice endomorphism, duality, order preserving mapping
Classification (MSC2000): 52A20
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Electronic version published on: 18 Sep 2008. This page was last modified: 28 Jan 2013.