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Deformation Theory ( Lecture Notes )

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    0098923 - MU-W 2008 RIV CZ eng J - Journal Article
    Doubek, M. - Markl, Martin - Zima, P.
    Deformation Theory ( Lecture Notes ).
    [Teorie deformací ( zápisy z přednášek ).]
    Archivum mathematicum. Roč. 43, č. 5 (2007), s. 333-371. ISSN 0044-8753.
    [Winter School Geometry and Physics/27./. Srní, 13.01.2007-20.01.2007]
    R&D Projects: GA ČR GA201/05/2117
    Institutional research plan: CEZ:AV0Z10190503
    Keywords : deformation * Mauerer-Cartan equation * strongly homotopy Lie algebra
    Subject RIV: BA - General Mathematics

    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.

    V článku jsou vysvětleny základní pojmy teorie deformací založené na Maurer-Cartanově rovnici.
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