9 research outputs found
The Nowicki Conjecture for free metabelian Lie algebras
Let be the polynomial algebra in variables
over a field of characteristic 0. The classical theorem of Weitzenb\"ock
from 1932 states that for linear locally nilpotent derivations (known
as Weitzenb\"ock derivations) the algebra of constants is
finitely generated. When the Weitzenb\"ock derivation acts on the
polynomial algebra in variables by ,
, , Nowicki conjectured that
is generated by and for all . There are
several proofs based on different ideas confirming this conjecture. Considering
arbitrary Weitzenb\"ock derivations of the free -generated metabelian Lie
algebra , with few trivial exceptions, the algebra is not
finitely generated. However, the vector subspace of the
commutator ideal of is finitely generated as a
-module. In this paper we study an analogue of the Nowicki
conjecture in the Lie algebra setting and give an explicit set of generators of
the -module .Comment: 8 page
Separating invariants for arbitrary linear actions of the additive group
We consider an arbitrary representation of the additive group G_a
over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants
Separating invariants for arbitrary linear actions of the additive group
We consider an arbitrary representation of the additive group G_a
over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants