Q-Groupoids and Their Cohomology

Authors

Rajan Amit Mehta, Washington University in St. LouisFollow

Document Type

Article

Publication Date

10-1-2009

Publication Title

Pacific Journal of Mathematics

Abstract

We approach Mackenzie's L{script}A{script}-groupoids from a supergeometric point of view by introducing Q-groupoids, which are groupoid objects in the category of Q-manifolds. There is a faithful functor from the category of L{script}A{script}-groupoids to the category of Q-groupoids. We associate to every Qgroupoid a double complex that provides a model for the Q-cohomology of the classifying space. As examples, we obtain models for equivariant Q-and orbifold Q-cohomology, and for equivariant Lie algebroid and orbifold Lie algebroid cohomology. We obtain double complexes associated to Poisson groupoids and groupoid-algebroid "matched pairs".

Keywords

Equivariant cohomology, Lie algebroids, Lie groupoids, Q-manifolds, Simplicial manifolds

Volume

242

Issue

2

First Page

311

Last Page

332

DOI

10.2140/pjm.2009.242.311

ISSN

00308730

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Mehta, Rajan Amit, "Q-Groupoids and Their Cohomology" (2009). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/94