Geodesic
Deformation Theory (Lecture Notes)
Archivum mathematicum, Tome 43 (2007) no. 5, pp. 333-371.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{ARM_2007__43_5_a3,
     author = {Doubek, M. and Markl, M. and Zima, P.},
     title = {Deformation {Theory} {(Lecture} {Notes)}},
     journal = {Archivum mathematicum},
     pages = {333--371},
     publisher = {mathdoc},
     volume = {43},
     number = {5},
     year = {2007},
     mrnumber = {2381782},
     zbl = {1199.13015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2007__43_5_a3/}
}
TY  - JOUR
AU  - Doubek, M.
AU  - Markl, M.
AU  - Zima, P.
TI  - Deformation Theory (Lecture Notes)
JO  - Archivum mathematicum
PY  - 2007
SP  - 333
EP  - 371
VL  - 43
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ARM_2007__43_5_a3/
LA  - en
ID  - ARM_2007__43_5_a3
ER  - 
%0 Journal Article
%A Doubek, M.
%A Markl, M.
%A Zima, P.
%T Deformation Theory (Lecture Notes)
%J Archivum mathematicum
%D 2007
%P 333-371
%V 43
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ARM_2007__43_5_a3/
%G en
%F ARM_2007__43_5_a3
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/