Journal of Symplectic Geometry

Q-algebroids and their cohomology

Rajan Amit Mehta

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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.

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

First available in Project Euclid: 13 August 2009

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Mehta, Rajan Amit. Q-algebroids and their cohomology. J. Symplectic Geom. 7 (2009), no. 3, 263--293.

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