28 citations · 44 across the 14 of their papers we have counts for
14 papers
Partial Poisson Lie groups and groupoids. Application to Von Neumann algebras
Fernand Pelletier, Patrick Cabau
The purpose of this paper is to propose a version of the notion of convenient Lie groupoid as a generalization of this concept in finite dimension. The authors point out which obst…
Partial Dirac Structures and Dynamical Systems
Fernand Pelletier, Patrick Cabau
In a previous paper (PeCa24), the notion of Dirac structure in finite dimension was extended to the convenient setting. In particular, we introduce the notion of \emph{partial Dira…
Partial Dirac structures in infinite dimension
Fernand Pelletier, Patrick Cabau
In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenie…
Partial Nambu-Poisson structures on a convenient manifold
Patrick Cabau, Fernand Pelletier
This paper offers an adaptation to the convenient setting of finite dimensional Nambu-Poisson structures. In particular, for partial Nambu structures, we look for those whose class…
Structure of finite dimensional linear bundles morphisms
Fernand Pelletier, Patrick Cabau
Let be a fibre bundle over the -dimensional manifold whose typical fibre is the vector space and let be a fibre bundle over the -di…
A survey on partial Nambu-Poisson structures in the convenient setting
Patrick Cabau, Fernand Pelletier
This paper is a survey (may be incomplete) on partial Nambu-Poisson structures in infinite dimension, mainly in the convenient setting. These ones can be seen as a generalization o…
Prolongations of convenient Lie algebroids
Patrick Cabau, Fernand Pelletier
We first define the concept of Lie algebroid in the convenient setting. In reference to the finite dimensional context, we adapt the notion of prolongation of a Lie algebroid over…
Projective limits of local shift morphism
Patrick Cabau
We define the notion of projective limit of local shift morphisms of type and endow the space of such mathematical objects with an adapted differential structu…
Projective and Direct limits of Banach and tensor structures
P. Cabau, F. Pelletier
We endow projective (resp. direct) limits of Banach tensor structures with Fréchet (resp. convenient) structures and study adapted connections to -structures in both frameworks.…
Convenient Partial Poisson Manifolds
F. Pelletier, P. Cabau
We introduce the concept of partial Poisson structure on a manifold modelled on a convenient space. This is done by specifying a (weak) subbundle of a…
Integrability on Direct Limit Banach manifolds
Patrick Cabau, Fernand Pelletier
This paper is devoted to the framework of direct limit of anchored Banach bundles over a convenient manifold which is a direct limit of Banach manifold. In particular we give a cri…
Geometric structure for the tangent bundle of direct limit manifolds
Ali Suri, Patrick Cabau
We equip the direct limit of tangent bundles of paracompact finite dimensional manifolds with a structure of convenient vector bundle with structural group $GL(\infty,\mathbb{R}) =…
Almost Lie structures on an anchored Banach bundle
Patrick Cabau, Fernand Pelletier
Under appropriate assumptions, we generalize the concept of linear almost Poisson struc- tures, almost Lie algebroids, almost differentials in the framework of Banach anchored bund…
Special Lagrangian manifolds obtained from complex Grassmannians
A. Ben Abdesselem, P. Cabau
This paper gives an example of special Lagrangian manifold obtained from a hypersurface of a complex Grassmannian with vanishing first Chern class. The obtained manifold is a 1-tor…