Modular classes of skew algebroid relations

Abstract

Skew algebroid is a natural generalization of the concept of Lie algebroid. In this paper, for a skew algebroid E, its modular class mod(E) is defined in the classical as well as in the supergeometric formulation. It is proved that there is a homogeneous nowhere-vanishing 1-density on E* which is invariant with respect to all Hamiltonian vector fields if and only if E is modular, i.e. mod(E)=0. Further, relative modular class of a subalgebroid is introduced and studied together with its application to holonomy, as well as modular class of a skew algebroid relation. These notions provide, in particular, a unified approach to the concepts of a modular class of a Lie algebroid morphism and that of a Poisson map.

20 pages

References in corpus (6)

• Tangent Lifts of Poisson and Related Structures
• Dirac Algebroids in Lagrangian and Hamiltonian Mechanics
• Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries
• Hamiltonian Dynamics on Lie Algebroids, Unimodularity and Preservation of Volumes
• Modular class of even symplectic manifolds
• The modular class of a Poisson map

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• Homological sections of Lie algebroids
• Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms
• The modular class of a Dirac map
• Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids