Modular Classes of Lie Groupoid Representations up to Homotopy

[摘要] 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''.

[关键词] Lie groupoid;representation up to homotopy;modular class