Generalized translation invariant valuations and the polytope algebra
| Autor: | Dmitry Faifman, Andreas Bernig |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Mathematics - Differential Geometry
0209 industrial biotechnology Computer Science::Computer Science and Game Theory Convex geometry Mathematics::Combinatorics General Mathematics 010102 general mathematics Subalgebra Polytope Metric Geometry (math.MG) 02 engineering and technology 01 natural sciences Integral geometry Algebra 020901 industrial engineering & automation Differential Geometry (math.DG) Mathematics - Metric Geometry FOS: Mathematics Mathematics::Metric Geometry 52B45 53C65 0101 mathematics Invariant (mathematics) General position Mathematics Vector space |
| Popis: | We study the space of generalized translation invariant valuations on a finite-dimensional vector space and construct a partial convolution which extends the convolution of smooth translation invariant valuations. Our main theorem is that McMullen's polytope algebra is a subalgebra of the (partial) convolution algebra of generalized translation invariant valuations. More precisely, we show that the polytope algebra embeds injectively into the space of generalized translation invariant valuations and that for polytopes in general position, the convolution is defined and corresponds to the product in the polytope algebra. 29 pages; minor changes |
| Databáze: | OpenAIRE |
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