Deformation theory of Courant algebroids via the Rothstein algebra

DOI10.1016/j.jpaa.2014.12.002zbMath1315.53103arXiv0807.0584OpenAlexW2016659000MaRDI QIDQ2341544

Stefan Waldmann, Frank Keller

Publication date: 24 April 2015

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.0584

zbMATH Keywords

deformation quantizationCourant algebroidsFedosov methodgraded Poisson algebrasLie-Rinehard pair

Mathematics Subject Classification ID

Deformation quantization, star products (53D55) Almost contact and almost symplectic manifolds (53D15)

Related Items (16)

Deformations of Courant algebroids and Dirac structures via blended structures ⋮ Courant-Dorfman algebras and their cohomology. ⋮ Generalized metric formulation of double field theory on group manifolds ⋮ Star products on graded manifolds and α′-corrections to Courant algebroids from string theory ⋮ Higher multi-Courant algebroids ⋮ Courant cohomology, Cartan calculus, connections, curvature, characteristic classes ⋮ Nijenhuis structures on Courant algebroids ⋮ Courant-Dorfman algebras of differential operators and Dorfman connections of Courant algebroids ⋮ Unnamed Item ⋮ Six-dimensional (1,0) superconformal models and higher gauge theory ⋮ Homotopy Loday Algebras and Symplectic $2$-Manifolds ⋮ Leibniz algebras with derivations ⋮ Deformation of hom-Lie-Rinehart algebras ⋮ Split Courant algebroids as \(L_\infty\)-structures ⋮ The standard cohomology of regular Courant algebroids ⋮ Deformations of Courant pairs and Poisson algebras

Cites Work

• Derived brackets
• Courant-Dorfman algebras and their cohomology.
• Formal deformations of Dirac structures
• Reduction of Courant algebroids and generalized complex structures
• Deformations of Lie brackets: Cohomological aspects
• Lie-Rinehart algebras, Gerstenhaber algebras and Batalin-Vilkovisky algebras
• Courant algebroids and strongly homotopy Lie algebras
• Homogeneous Fedosov star products on cotangent bundles. II: GNS representations, the WKB expansion, traces, and applications
• Remarks on the definition of a Courant algebroid
• Deformation quantization of Poisson manifolds
• Completely positive inner products and strong Morita equivalence
• On the deformation of rings and algebras
• Poisson-Geometrie und Deformationsquantisierung
• Poisson cohomology and quantization.
• Dirac Manifolds
• Differential Forms on General Commutative Algebras
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