Journal of Symplectic Geometry

Q-algebroids and their cohomology

Rajan Amit Mehta

Full-text: Open access

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.

Article information

Source
J. Symplectic Geom., Volume 7, Number 3 (2009), 263-293.

Dates
First available in Project Euclid: 13 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1250169193

Mathematical Reviews number (MathSciNet)
MR2534186

Zentralblatt MATH identifier
1215.22002

Citation

Mehta, Rajan Amit. Q-algebroids and their cohomology. J. Symplectic Geom. 7 (2009), no. 3, 263--293. https://projecteuclid.org/euclid.jsg/1250169193


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