Remarks on uniform bundles on projective spaces

On projective spaces of dimension \(d\ge 2\) defined over a field of positive characteristic we construct rank \(d+1\) uniform toric but non-homogeneous bundles, which do not exists in characteristic zero. These bundles are obtained by choosing suitable equivariant extensions of the Frobenius pullbacks of \(T_{\mathbb {P}^d}\) by a line bundle.