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Higher derived brackets and homotopy algebras
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General theory of Lie groupoids and Lie algebroids (London Mathematical Society Lecture Note Series 213)
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Graded Manifolds and Drinfeld Doubles for Lie Bialgebroids
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…
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Q-Manifolds and Mackenzie Theory
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…
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$Q$-manifolds and Higher Analogs of Lie Algebroids
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…
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Higher Derived Brackets for Arbitrary Derivations
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…
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Geometric Integration Theory on Supermanifolds
Higher Poisson Brackets and Differential Forms
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…
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On a non-Abelian Poincaré lemma
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…
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Quantization of Forms on the Cotangent Bundle
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…
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