منابع مشابه
Homology and modular classes of Lie algebroids
For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evens, J.-H. Lu, and A. Weinstein.
متن کاملPoisson 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.
متن کاملModular Classes of Loday Algebroids
We introduce the concept of Loday algebroids, a generalization of Courant algebroids. We define the naive cohomology and modular class of a Loday algebroid, and we show that the modular class of the double of a Lie bialgebroid vanishes. For Courant algebroids, we describe the relation between the naive and standard cohomologies and we conjecture that they are isomorphic when the Courant algebro...
متن کاملLie Algebroids, Holonomy and Characteristic Classes
We extend the notion of connection in order to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual concept of a covariant connection. It allows us to define holonomy of the orbit foliation of a Lie algebroid and prove a Stability Theorem. We also introduce secondary or exotic characteristic classes, thus pr...
متن کاملInvariants of Lie algebroids
Several new invariants of Lie algebroids have been discovered recently. We give an overview of these invariants and establish several relationships between them.
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2005
ISSN: 1631-073X
DOI: 10.1016/j.crma.2005.09.010