Geodesic
Deformation Theory (Lecture Notes)
Archivum mathematicum, Tome 43 (2007) no. 5, pp. 333-371 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation between deformations and solutions of the corresponding Maurer-Cartan equation. In Section  we generalize the Maurer-Cartan equation to strongly homotopy Lie algebras and prove the homotopy invariance of the moduli space of solutions of this equation. In the last section we indicate the main ideas of Kontsevich’s proof of the existence of deformation quantization of Poisson manifolds.
First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation between deformations and solutions of the corresponding Maurer-Cartan equation. In Section  we generalize the Maurer-Cartan equation to strongly homotopy Lie algebras and prove the homotopy invariance of the moduli space of solutions of this equation. In the last section we indicate the main ideas of Kontsevich’s proof of the existence of deformation quantization of Poisson manifolds.
Classification : 13D10, 14D15, 46L65, 53D55
Keywords: deformation; Maurer-Cartan equation; strongly homotopy Lie algebra; deformation quantization 
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Doubek, M.; Markl, M.; Zima, P. Deformation Theory (Lecture Notes). Archivum mathematicum, Tome 43 (2007) no. 5, pp. 333-371. http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a3/

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