Kumpera-Ruiz algebras in Goursat flags are optimal in small lengths

Mormul, Piotr

doi:10.1007/s10958-005-0347-0

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…Moreover, in case non-vanishing constants do appear in the models with a specific given code, their non-equivalence classes can eventually be parametrized by these constants, which is the case above. Such an approach can be found in [38] though treated in a very different setting and only in a rather specific case where the number 3 does not appear in the code i.e., the flag being therefore free of any inversion.…”

Section: Equations Defining Gmentioning

confidence: 99%

Automorphisms of flag systems

Kumpera

2019

Journal of Differential Equations

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We first discuss the problems in the theory of ordinary differential equations that gave rise to the concept of a flag system and illustrate these with the Cartan criterion for Monge equations (1st order) as well as the Cartan statement concerning the local equivalence of Monge-Ampère type equations (2nd order). Next, we describe a prolongation functor operating on the infinitesimal symmetries (automorphisms) of the Darboux flag and extending these, isomorphically, to all the symmetries of any other flag. Hence, flag systems cannot be distinguished by their symmetry algebras and the local classification of these objects is approached by considering higher order isotropies of these algebras as well as the groupoids of k − th order formal equivalences since the differential equations defining the latter provide precious information for the application of flag systems to differential equations (e.g., Cartan's criterion for non-linear Monge equations). In examining the behaviour of the isotropy algebras, that can either diminish or remain the same, when passing from a derived system Sν to the previous system S ν−1 , we obtain a full set of numerical invariants for the elementary flag systems that moreover specify the local models. flag systems and models and infinitesimal automorphisms and isotropy and Darboux prolongations and k − th order equivalence groupoids.

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Section: Equations Defining Gmentioning

confidence: 99%