Actions of automorphisms groups on Weil bundles

In this work the irreductibility of the Weil algebra is proved and the notion of the Whitney sum of the Weil algebra is introduced. It is proved that if $m$ is a width, $k$ — a radical dimension, $r$ — a Weil algebra index, then the dimension of automorphism group of this algebra equals $mk-r$. The left and right actions of the automorphism group of the Weil algebra are constructed on the Weil bundle.