1,693 research outputs found
Nijenhuis and Compatible Tensors on Lie and Courant algebroids
We show that well known structures on Lie algebroids can be viewed as
Nijenhuis tensors or pairs of compatible tensors on Courant algebroids. We
study compatibility and construct hierarchies of these structures
Dirac pairs
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-Hamiltonian structure vanishes. Following Gelfand and Dorfman,
we then define Dirac pairs, and we analyze the relationship of this general
notion with the various kinds of compatible structures on manifolds, more
generally on Lie algebroids.Comment: dedicated to Tudor Ratiu, 23 page
Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey
After a brief summary of the main properties of Poisson manifolds and Lie
algebroids in general, we survey recent work on the modular classes of Poisson
and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted
Poisson structure, and of Poisson-Nijenhuis manifolds. A review of the spinor
approach to the modular class concludes the paper.Comment: Dedicated to the memory of Thomas Branson. This is a contribution to
the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P.
Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods
and Applications) at http://www.emis.de/journals/SIGMA
Relative modular classes of Lie algebroids
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.Comment: 8 page
Lie algebroids and Poisson-Nijenhuis structures
Poisson-NIjenhuis structures for an arbitrary Lie agebroid are defined and
studied by means of tangent lifts of tensor fields.Comment: Latex, 15 pages. To appear in Reports on Mathematical Physics (vol
40, 1997
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