205 citations · 285 across the 21 of their papers we have counts for
9 papers · 1 filter
Dirac pairs
Yvette Kosmann-Schwarzbach
We extend the definition of the Nijenhuis torsion of an endomorphism of a Lie algebroid to that of a relation, and we prove that the torsion of the relation defined by a bi-Hamilto…
Nijenhuis structures on Courant algebroids
Yvette Kosmann-Schwarzbach
We study Nijenhuis structures on Courant algebroids in terms of the canonical Poisson bracket on their symplectic realizations. We prove that the Nijenhuis torsion of a skew-symmet…
Compatible structures on Lie algebroids and Monge-Ampère operators
Yvette Kosmann-Schwarzbach, Vladimir Rubtsov
We study pairs of structures, such as the Poisson-Nijenhuis structures, on the tangent bundle of a manifold or, more generally, on a Lie algebroid or a Courant algebroid. These com…
Modular classes of Lie algebroid morphisms
Yvette Kosmann-Schwarzbach, Camille Laurent-Gengoux, Alan Weinstein
We study the behavior of the modular class of a Lie algebroid under general Lie algebroid morphisms by introducing the relative modular class. We investigate the modular classes of…
Relative modular classes of Lie algebroids
Yvette Kosmann-Schwarzbach, Alan Weinstein
We study the relative modular classes of Lie algebroids, and we determine their relationship with the modular classes of Lie algebroids with a twisted Poisson structure.
Derived brackets
Yvette Kosmann-Schwarzbach
We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the…
Differential operators and actions of Lie algebroids
Y. Kosmann-Schwarzbach, K. C. H. Mackenzie
We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representations of a Lie group on a vector bundle, and related conc…
Quasi-Poisson Manifolds
Anton Alekseev, Yvette Kosmann-Schwarzbach, Eckhard Meinrenken
A quasi-Poisson manifold is a G-manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in $\wedge^3 \g$…
Manin pairs and moment maps
Anton Alekseev, Yvette Kosmann-Schwarzbach
A Lie group G in a group pair (D,G), integrating a Lie algebra g in a Manin pair (d,g) has a quasi-Poisson structure. We define the quasi-Poisson actions of such Lie groups G, that…