Q-algebroids and their cohomology
By R. Mehta. 2007
48 citations recorded by the source corpus.
A Q-algebroid is a Lie superalgebroid 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 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d5f8a126b5ef281810a388a458851f37becfddf6
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Citations in the corpus
- Representations up to homotopy of Lie algebroids (2009, methodology): “ated, we stress that our notion of representation up to homotopy differs fundamentally from the one used in their paper. Our Weil algebra is probably isomorphic to the one given by Mehta in his thesis [24], where, using the language of supermanifolds, he described the algebra(C∞([−1]T([−1]A)),Ld A +d”
- The Atiyah class of a dg-vector bundle (2015, background): “Given a vector bundle E π → M of graded manifolds, its space of sections, denoted Γ(E), is defined to be ⊕ j∈Z Γj(E), where Γj(E) consists of degree preserving maps s ∈ Hom(M, E [−j]) such that (π[−j]) ◦ s = idM, where π[−j] : E [−j] → M is the natural map induced from π; see [10] for more details.”