We define graded manifolds as a version of supermanifolds endowed with an extra Z-grading in the structure sheaf, called weight (not linked
with parity). Examples are ordinary supermanifolds, vector… Expand

Double Lie algebroids were discovered by Kirill Mackenzie from the study of double Lie groupoids and were defined in terms of rather complicated conditions making use of duality theory for Lie… Expand

We show how the relation between Q‐manifolds and Lie algebroids extends to “higher” or “non‐linear” analogs of Lie algebroids. We study the identities satisfied by a new algebraic structure that… Expand

We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie… Expand

We show how the relation between Poisson brackets and symplectic forms can be extended to the case of inhomogeneous multivector fields and inhomogeneous differential forms (or pseudodifferential… Expand

We show that a well-known result on solutions of the Maurer--Cartan equation extends to arbitrary (inhomogeneous) odd forms: any such form with values in a Lie superalgebra satisfying $d\o+\o^2=0$ is… Expand

Abstract:We consider the following construction of quantization. For a Riemannian manifold $M$ the space of forms on T⋆M is made into a space of (full) symbols of operators acting on forms on M. This… Expand