We give an algorithm to write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent invariant operators of order up to k. The independent differential operators of second order are three and we give an explicit realization of them. The appli...

We consider the problem of obtaining conformally invariant differential operators in Minkowski space. We show that the conformal electrodynamics equations and the gauge transformations for them can be obtained in the frame of the method of dimensional reduction developed in the first part of the paper. We describe a method for obtaining a large set of conformally invariant differential operator...

We give an algorithm write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent invariant operators of order up to k. The independent differential operators of second order are three and we give an explicit realization of them. The applied ...

We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of se...

The primary goal of this paper is to provide a rigorous theoretical justification of Cartan’s method of moving frames for arbitrary finite-dimensional Lie group actions on manifolds. The general theorems are based a new regularized version of the moving frame algorithm, which is of both theoretical and practical use. Applications include a new approach to the construction and classification of ...