2000 Mathematics Subject Classification: 13N15, 13A50, 13F20. An analogue of the symbolic method of classical invariant theory for a representation and manipulation of the elements of the kernel of Weitzenböck derivations is developed.
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.
2000 Mathematics Subject Classification: 13N15, 13A50, 16W25. By using classical invariant theory approach, formulas for computation of the Poincaré series of the kernel of linear locally nilpotent derivations are found.
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