On a non-Abelian Poincaré lemma

DOI10.1090/S0002-9939-2011-11116-XzbMath1282.58007arXiv0905.0287WikidataQ124879113 ScholiaQ124879113MaRDI QIDQ2845560

Theodore Th. Voronov

Publication date: 2 September 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.0287

zbMATH Keywords

differential formsLie algebroidsLie superalgebrassupermanifoldsMaurer-Cartan equation\(Q\)-manifoldsmultiplicative integralhomological vector fieldsQuillen's connection

Mathematics Subject Classification ID

Nonabelian homological algebra (category-theoretic aspects) (18G50) Supermanifolds and graded manifolds (58A50) Superalgebras (17A70) Graded Lie (super)algebras (17B70) Pseudogroups and differentiable groupoids (58H05) Analysis on supermanifolds or graded manifolds (58C50)

Related Items (10)

Minimal models of quantum homotopy Lie algebras via the BV-formalism ⋮ Higher Poincaré lemma and integrability ⋮ Gauge PDE and AKSZ‐type Sigma Models ⋮ Graded Geometry, Q‐Manifolds, and Microformal Geometry ⋮ Notes on the \(L_\infty\)-approach to local gauge field theories ⋮ Normal forms of \(\mathbb{Z}\)-graded \(Q\)-manifolds ⋮ Higher-order analogs of Lie algebroids via vector bundle comorphisms ⋮ Characteristic classes associated to Q-bundles ⋮ Microformal geometry and homotopy algebras ⋮ The Poincaré lemma, antiexact forms, and fermionic quantum harmonic oscillator

Cites Work

• Superconnections and the Chern character
• The Lie algebra structure of tangent cohomology and deformation theory
• \(Q\)-manifolds and Mackenzie theory
• Feynman diagrams and minimal models for operadic algebras
• Lie algebroids and homological vector fields
• Drinfel’d doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids
• $Q$-manifolds and Higher Analogs of Lie Algebroids
• Characteristic classes associated to Q-bundles
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