Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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”.
Lie groupoid; representation up to homotopy; modular class
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) is a peer-reviewed open access journal.
Mehta, Rajan Amit, "VB-Groupoids and Representation Theory of Lie Groupoids" (2015). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.