Linear natural liftings of forms to Weil bundles with Weil algebras ${\mathbb D}^r_k$

Abstract: We give an explicit description and calculate the dimension of the vector space of linear natural liftings of

p

-forms on

n

-dimensional manifolds

M

to

q

-forms on

T^{{m a t h b b D}_{k}^{r}} M

, where

{m a t h b b D}_{k}^{r}

is the Weil algebra of

r

-jets at 0 of smooth functions

{m a t h b b R}^{k} l o n g r i g h t a r r o w m a t h b b R

, for all non-negative integers

n

,

p

,

q

,

r

,

k

except the case

p = n

and

q = 0

.