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- Title
DEFORMATION THEORY (LECTURE NOTES).
- Authors
Doubek, M.; Markl, M.; Zima, P.
- Abstract
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.
- Subjects
ASSOCIATIVE algebras; ALGEBRA; HOMOLOGY theory; HOMOTOPY theory; LIE algebras; POISSON manifolds
- Publication
Archivum Mathematicum, 2007, Vol 43, Issue 5, p333
- ISSN
0044-8753
- Publication type
Article