Invariants of algebraic group actions from differential point of view

Natural differential invariants and equivalence of nonlinear second order differential operators

“…We proposed in ( [9], [11]) methods of finding algebraic invariants by using differential invariants. Thus, this paper, in some sense, conclude the interplay between differential and algebraic invariants.…”

“…In the previous publications ( [10], [9], [11]), we discussed applications of differential invariants to finding of the algebraic ones. It is related to differences between ) and Lie-Tresse theorems ( [7]), describing the structures of algebras of algebraic and differential invariants.…”

On Metric Invariants of Spherical Harmonics

“…In [1,2], we tried to reconcile these theories and have shown that the correct formulation of the basic theorems in the theory of differential invariants, such as the Lie-Tresse theorem, essentially requires the algebraic theory and, on the other hand, the use of differential invariants in pure algebraic problems could also be successful.…”