Modular Classes of Lie Groupoid Representations up to Homotopy

Abstract

We describe a construction of the modular class associated to a representation up to homotopy of a Lie groupoid. In the case of the adjoint representation up to homotopy, this class is the obstruction to the existence of a volume form, in the sense of Weinstein's "The volume of a differentiable stack".

References in corpus (4)

• Supergroupoids, double structures, and equivariant cohomology
• VB-groupoids and representation theory of Lie groupoids
• Lie algebroid modules and representations up to homotopy
• Ehresmann doubles and Drinfel'd doubles for Lie algebroids and Lie bialgebroids

Cited by in corpus (2)

• Poisson structures of divisor-type
• Obstructions to representations up to homotopy and ideals