Modular classes revisited

Abstract

We present a graded-geometric approach to modular classes of Lie algebroids and their generalizations, introducing in this setting an idea of relative modular class of a Dirac structure for a certain type of Courant algebroids, called projectable. This novel approach puts several concepts related to Poisson geometry and its generalizations in a new light and simplifies proofs. It gives, in particular, a nice geometric interpretation of modular classes of twisted-Poisson structures on Lie algebroids.

10 pages, slightly revised version to appear in Int. J. Geom. Meth. Mod. Phys

References in corpus (5)

• Dirac Algebroids in Lagrangian and Hamiltonian Mechanics
• Modular classes of skew algebroid relations
• On higher analogues of Courant algebroids
• Jacobi-Nijenhuis algebroids and their modular classes
• Modular classes of Poisson-Nijenhuis Lie algebroids

Cited by in corpus (3)

• Pre-Courant Algebroids
• Courant cohomology, Cartan calculus, connections, curvature, characteristic classes
• Modular Classes of Q-Manifolds, Part II: Riemannian Structures & Odd Killing Vectors Fields