Q-Algebroids and Their Cohomology

Authors

Rajan Amit Mehta, Washington University in St. LouisFollow

Document Type

Article

Publication Date

1-1-2009

Publication Title

Journal of Symplectic Geometry

Abstract

A Q-algebroid is a graded Lie algebroid equipped with a compatible homological vector field and is the infinitesimal object corresponding to a Q-groupoid. We associate to every Q-algebroid a double complex. As a special case, we define the Becchi-Rouet-Stora-Tyutin (BRST) model of a Lie algebroid, which generalizes the BRST model for equivariant cohomology. We extend to this setting the Mathai-Quillen-Kalkman isomorphism of the BRST and Weil models, and we suggest a definition of a basic subcomplex which, however, requires a choice of a connection. Other examples include Roytenberg's homological double of a Lie bialgebroid, Ginzburg's model of equivariant Lie algebroid cohomology, the double of a Lie algebroid matched pair, and Q-algebroids arising from lifted actions on Courant algebroids.

Volume

7

Issue

3

First Page

263

Last Page

293

DOI

10.4310/JSG.2009.v7.n3.a1

ISSN

15275256

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Mehta, Rajan Amit, "Q-Algebroids and Their Cohomology" (2009). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/95