2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.We reduce the Nowicki conjecture on Weitzenböck derivations of polynomial algebras to a well known problem of classical invariant theory.
Many infinite finitely generated ideal-simple commutative semirings are additively idempotent. It is not clear whether this is true in general. However, to solve the problem, one can restrict oneself only to parasemifields.
We study the free complexification operation for compact quantum groups, . We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free unitary quantum groups satisfying .
If is a smooth scheme over a perfect field of characteristic , and if is the sheaf of differential operators on [7], it is well known that giving an action of on an -module is equivalent to giving an infinite sequence of -modules descending via the iterates of the Frobenius endomorphism of [5]. We show that this result can be generalized to any infinitesimal deformation of a smooth morphism in characteristic , endowed with Frobenius liftings. We also show that it extends to adic...