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Deformation Theory of Algebras and Their Diagrams

Martin Markl Academy of Sciences of the Czech Republic, Praha, Czech Republic
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-0-8218-8979-4
Product Code: CBMS/116
129 pp
List Price: $38.00 Individual Price:$30.40
Electronic ISBN: 978-0-8218-9192-6
Product Code: CBMS/116.E
129 pp
List Price: $35.00 MAA Member Price:$31.50
AMS Member Price: $28.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$57.00
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Deformation Theory of Algebras and Their Diagrams
Martin Markl Academy of Sciences of the Czech Republic, Praha, Czech Republic
A co-publication of the AMS and CBMS
Available Formats:
 Softcover ISBN: 978-0-8218-8979-4 Product Code: CBMS/116 129 pp
 List Price: $38.00 Individual Price:$30.40
 Electronic ISBN: 978-0-8218-9192-6 Product Code: CBMS/116.E 129 pp
 List Price: $35.00 MAA Member Price:$31.50 AMS Member Price: $28.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$57.00
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 1162012
MSC: Primary 13; 14; Secondary 53; 55;

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.

A co-publication 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 Maurer-Cartan 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

• Request Review Copy
Volume: 1162012
MSC: Primary 13; 14; Secondary 53; 55;

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.

A co-publication 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 Maurer-Cartan 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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