Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 2, pp. 541547 (2008) 

The endomorphisms of the lattice of closed convex conesRolf SchneiderMathematisches Institut, AlbertLudwigsUniversität, 79104 Freiburg i. Br., Germany, email: rolf.schneider@math.unifreiburg.deAbstract: 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 Full text of the article:
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