48 citations · 88 across the 7 of their papers we have counts for
7 papers
Quasi-Lie schemes for PDEs
Jose F. Carinena, Janusz Grabowski, Javier de Lucas
The theory of quasi-Lie systems, i.e. systems of first order ordinary differential equations which can be related via a generalised flow to Lie systems, is extended to systems of p…
Solvability of a Lie algebra of vector fields implies their integrability by quadratures
J. F. Cariñena, F. Falceto, J. Grabowski
We present a substantial generalisation of a classical result by Lie on integrability by quadratures. Namely, we prove that all vector fields in a finite-dimensional transitive and…
New developments in geometric mechanics
A. J. Bruce, K. Grabowska, J. Grabowski +1
We review the concept of a graded bundle, which is a generalisation of a vector bundle, its linearisation, and a double structure of this kind. We then present applications of thes…
Geometry of Lie integrability by quadratures
J. F. Cariñena, F. Falceto, J. Grabowski +1
In this paper we extend the Lie theory of integration in two different ways. First we consider a finite dimensional Lie algebra of vector fields and discuss the most general condit…
Lie superalgebras of differential operators
J. Grabowski, A. Kotov, N. Poncin
We describe explicitly Lie superalgebra isomorphisms between the Lie superalgebras of first-order superdifferential operators on supermanifolds, showing in particular that any such…
Nonholonomic Constraints: a New Viewpoint
J. Grabowski, M. de Leon, J. C. Marrero +1
The purpose of this paper is to show that, at least for Lagrangians of mechanical type, nonholonomic Euler-Lagrange equations for a nonholonomic linear constraint D may be viewed a…