Deformation Theory (lecture notes)

Details Deformation Theory (lecture notes) Deformation Theory (lecture notes)

2007-05-25

arxiv.org/abs/0705.3719v3

Archivum mathematicum 43(5), 2007, 333-371

Mathematics

Algebraic Geometry

42 pages, false warning on page 35 removed

Scientific paper

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 6 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.

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