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Deformation Theory ( Lecture Notes )
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SYSNO ASEP 0098923 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Ostatní články Title Deformation Theory ( Lecture Notes ) Title Teorie deformací ( zápisy z přednášek ) Author(s) Doubek, M. (CZ)
Markl, Martin (MU-W) RID, SAI, ORCID
Zima, P. (CZ)Source Title Archivum mathematicum. - : Masarykova univerzita - ISSN 0044-8753
Roč. 43, č. 5 (2007), s. 333-371Number of pages 39 s. Action Winter School Geometry and Physics/27./ Event date 13.01.2007-20.01.2007 VEvent location Srní Country CZ - Czech Republic Event type WRD Language eng - English Country CZ - Czech Republic Keywords deformation ; Mauerer-Cartan equation ; strongly homotopy Lie algebra Subject RIV BA - General Mathematics R&D Projects GA201/05/2117 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10190503 - MU-W (2005-2011) Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2008
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