Modules of principal parts on the projective line

The modules of principal partsP ^k (E) of a locally free sheaf ε on a smooth schemeX is a sheaf ofO _X -bimodules which is locally free as left and rightO _X -module. We explicitly split the modules of principal partsP ^k (O(n)) on the projective line in arbitrary characteristic, as left and rightO _p1-modules. We get examples when the splitting-type as left module differs from the splitting-type as right module. We also give examples showing that the splitting-type of the principal parts changes with the characteristic of the base field. Research supported by the EAGER foundation, the Emmy Noether research institute for mathematics, the Minerva foundation of Germany and the excellency centerGroup theoretic methods in the study of algebraic varieties.