Prykarpatsky A. On invariant differential ideals and homomorphic representations of functional derivations in differential rings (abstract)

Speaker: Anatolij Prykarpatsky

Title: On invariant differential ideals and homomorphic representations of functional derivations in differential rings

Abstract:
We analyze finitely-generated by some differntial-algebraic relationships differential ideals in functional rings, invariant with respect some specially constructed derivations and satisfying the corresponding Lie-algebraic relationships. Taking into account the finite-dimensionality of these ideals, we construct the suitably defined homomorphic Lax type representations of these derivations, which in some cases are reduced to constraints equivalent to differential-algebraic relationships on a generating function. The work in part generalizes the results devised before for proving integrability of the well known generalized hierarchy of the Riemann type equations. We have also reformulated by means of the differential-algebraic terms the well known Dubrovin's integrability criterion of the classical Riemann equations, perturbed by means of some special terms from a suitably constructed differential ring.

For more details see here.

Video
Slides: PrykarpatskyAMVconf2021slides.pdf

Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.