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Centroid and difference bodies define SL(n) equivariant operators on convex bodies and these operators are valuations with respect to Minkowski addition. We derive a classification of SL(n) equivariant Minkowski valuations and give a characterization of these operators. We also derive a classification of SL(n) contravariant Minkowski valuations and of L p -Minkowski valuations.doi:10.1090/s0002-9947-04-03666-9 fatcat:xcsayff47ncvjemfvt43qwxl5y