Deformation Theory (Lecture Notes)

M. Doubek; Martin Markl; Petr Zima

Archivum Mathematicum (2007)

  • Volume: 043, Issue: 5, page 333-371
  • ISSN: 0044-8753

Abstract

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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.

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Doubek, M., Markl, Martin, and Zima, Petr. "Deformation Theory (Lecture Notes)." Archivum Mathematicum 043.5 (2007): 333-371. <http://eudml.org/doc/250171>.

@article{Doubek2007,
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  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.},
author = {Doubek, M., Markl, Martin, Zima, Petr},
journal = {Archivum Mathematicum},
keywords = {deformation; Maurer-Cartan equation; strongly homotopy Lie algebra; deformation quantization; deformation; Maurer-Cartan equation; strongly homotopy Lie algebra; deformation quantization},
language = {eng},
number = {5},
pages = {333-371},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Deformation Theory (Lecture Notes)},
url = {http://eudml.org/doc/250171},
volume = {043},
year = {2007},
}

TY - JOUR
AU - Doubek, M.
AU - Markl, Martin
AU - Zima, Petr
TI - Deformation Theory (Lecture Notes)
JO - Archivum Mathematicum
PY - 2007
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 043
IS - 5
SP - 333
EP - 371
AB - 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.
LA - eng
KW - deformation; Maurer-Cartan equation; strongly homotopy Lie algebra; deformation quantization; deformation; Maurer-Cartan equation; strongly homotopy Lie algebra; deformation quantization
UR - http://eudml.org/doc/250171
ER -

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