Deformation theory of algebras and their diagrams
- Martin Markl.
- Uniform Title
- Lectures. Selections
- Providence, Rhode Island : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 
- Physical description
- ix, 129 pages : illustrations ; 26 cm.
- Regional conference series in mathematics ; no. 116.
Science Library (Li and Ma)
|QA1 .R33 NO.116||Unknown|
- Markl, Martin, 1960- author.
- Conference Board of the Mathematical Sciences sponsoring body.
- NSF-CBMS Regional Conference in the Mathematical Sciences on Deformation Theory of Algebras and Modules (2011 : Raleigh, N.C.)
- Includes bibliographical references.
- Publisher's Summary
- This book brings together both the classical and current aspects of deformation theory. The presentation is mostly self-contained, assuming only basic knowledge of commutative algebra, homological algebra and category theory. In the interest of readability, some technically complicated proofs have been omitted when a suitable reference was available. The relation between the uniform continuity of algebraic maps and topologized tensor products is explained in detail, however, as this subject does not seem to be commonly known and the literature is scarce. The exposition begins by recalling Gerstenhaber's classical theory for associative algebras. The focus then shifts to a homotopy-invariant setup of Maurer-Cartan moduli spaces. As an application, Kontsevich's approach to deformation quantization of Poisson manifolds is reviewed. Then, after a brief introduction to operads, a strongly homotopy Lie algebra governing deformations of (diagrams of) algebras of a given type is described, followed by examples and generalizations.
(source: Nielsen Book Data)9780821889794 20160609
- Algebra, Homological > Congresses.
- Commutative algebra -- Homological methods -- Deformations and infinitesimal methods.
- Algebraic geometry -- Families, fibrations -- Formal methods; deformations.
- Differential geometry -- Symplectic geometry, contact geometry -- Deformation quantization, star products.
- Algebraic topology -- Homology and cohomology theories -- Other homology theories.
- Publication date
- Copyright date
- Conference Board of the Mathematical Sciences CBMS. Regional conference series in mathematics ; number 116
- Covers ten lectures given by the author at the NSF-CBMS Regional Conference in the Mathematical Sciences on Deformation Theory of Algebras and Modules held at North Carolina State University, Raleigh, NC, May 16-20, 2011.
- 9780821889794 (alk. paper)
- 0821889796 (alk. paper)
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