4 papers
The category of -graded manifolds: what happens if you do not stay positive
Alexei Kotov, Vladimir Salnikov
In this paper we discuss the categorical properties of -graded manifolds. We start by describing the local model paying special attention to the differences in comparis…
Generalized and graded geometry for mechanics: a comprehensive introduction
Vladimir Salnikov, Aziz Hamdouni, Daria Loziienko
In this paper we make an overview of results relating the recent "discoveries" in differential geometry, such as higher structures and differential graded manifolds with some natur…
Differential graded Lie groups and their differential graded Lie algebras
Benoit Jubin, Alexei Kotov, Norbert Poncin +1
In this paper we discuss the question of integrating differential graded Lie algebras (DGLA) to differential graded Lie groups (DGLG). We first recall the classical problem of inte…
From modelling of systems with constraints to generalized geometry and back to numerics
Vladimir Salnikov, Aziz Hamdouni
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss doub…