Modular Classes of Loday Algebroids

Abstract

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 algebroid is transitive.

7 pages

References in corpus (4)

• Algebroids - general differential calculi on vector bundles
• Leibniz algebroid associated with a Nambu-Poisson structure
• On the structure of graded symplectic supermanifolds and Courant algebroids
• Duality for Lie-Rinehart algebras and the modular class

Cited by in corpus (18)

• On Regular Courant Algebroids
• H-twisted Lie algebroids
• Courant-Dorfman algebras and their cohomology
• On higher analogues of Courant algebroids
• The Pontryagin Class for Pre-Courant Algebroids
• Pre-Courant Algebroids
• Courant cohomology, Cartan calculus, connections, curvature, characteristic classes
• Courant algebroids: Cohomology and Matched Pairs
• H-twisted Courant algebroids
• Some generalizations of the notion of Lie algebra
• Lie Algebroids in the Loday-Pirashvili Category
• Dissections and automorphisms of regular Courant algebroids
• On hypersurfaces of generalized Kähler manifolds
• H-standard cohomology for Courant-Dorfman algebras and Leibniz algebras
• 'Anti-Commutable' Pre-Leibniz Algebroids and Admissible Connections
• The Free Courant Algebroid
• Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids
• The standard cohomology of regular Courant algebroids