Let $\mathfrak{L}_{0}^{r}$ be the set of all differentiable tensor fields of type $(r,0)$ defined on a differentiable manifold: in this paper the Author generalizes the bracket operation defined on $\mathfrak{L}_{0}^{1}$ and therefore he makes the direct sum of the family $(\mathfrak{L}_{0}^{i})_{i \in N}$ into a Lie algebra over the real number field.