Softcover ISBN:  9780821889794 
Product Code:  CBMS/116 
List Price:  $38.00 
Individual Price:  $30.40 
Electronic ISBN:  9780821891926 
Product Code:  CBMS/116.E 
List Price:  $35.00 
MAA Member Price:  $31.50 
AMS Member Price:  $28.00 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 116; 2012; 129 ppMSC: Primary 13; 14; Secondary 53; 55;
This book brings together both the classical and current aspects of deformation theory. The presentation is mostly selfcontained, 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 homotopyinvariant setup of MaurerCartan 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.A copublication of the AMS and CBMS.
ReadershipGraduate students and research mathematicians interested in deformations of algebras, moduli spaces, algebraic geometry, and/or algebraic topology.

Table of Contents

Chapters

Chapter 1. Basic notions

Chapter 2. Deformations and cohomology

Chapter 3. Finer structures of cohomology

Chapter 4. The gauge group

Chapter 5. The simplicial MaurerCartan space

Chapter 6. Strongly homotopy Lie algebras

Chapter 7. Homotopy invariance and quantization

Chapter 8. Brief introduction to operads

Chapter 9. $L_\infty $algebras governing deformations

Chapter 10. Examples

11. Index


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This book brings together both the classical and current aspects of deformation theory. The presentation is mostly selfcontained, 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 homotopyinvariant setup of MaurerCartan 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.
A copublication of the AMS and CBMS.
Graduate students and research mathematicians interested in deformations of algebras, moduli spaces, algebraic geometry, and/or algebraic topology.

Chapters

Chapter 1. Basic notions

Chapter 2. Deformations and cohomology

Chapter 3. Finer structures of cohomology

Chapter 4. The gauge group

Chapter 5. The simplicial MaurerCartan space

Chapter 6. Strongly homotopy Lie algebras

Chapter 7. Homotopy invariance and quantization

Chapter 8. Brief introduction to operads

Chapter 9. $L_\infty $algebras governing deformations

Chapter 10. Examples

11. Index