Linear Liftings of Skew-Symmetric Tensor Fields to Weil Bundles

Abstract

We define equivariant tensors for every non-negative integer p and every Weil algebra A and establish a one-to-one correspondence between the equivariant tensors and linear natural operators lifting skew-symmetric tensor fields of type (p, 0) on an n-dimensional manifold M to tensor fields of type (p, 0) on T A M if 1 ≤ p ≤ n. Moreover, we determine explicitly the equivariant tensors for the Weil algebras $$\mathbb{D}_k^r$$ , where k and r are non-negative integers.