BEIFANG Chen - Minkowski algebra of convex sets

The Minkowski algebra of convex sets is the vector space generated by characteristic functions of closed convex sets and relatively open convex sets, where the multiplication is induced by the Minkowski sum of convex bodies. The homomorphisms, sub-algebras, units, and embedding of this algebra will be studied. The Euler-Radon transform with respect to the Euler measure is considered, and have shown it is injective. This injectivity solves a syzygy problem on affine Grassmannians. The purpose to study Minkowski algebra is to set up a general framework so that mixed volume theory and integral geometry can be developed algebraically.