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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
Deformation Theory of Algebras and Their Diagrams
Softcover ISBN:  978-0-8218-8979-4
Product Code:  CBMS/116
List Price: $40.00
Individual Price: $32.00
eBook ISBN:  978-0-8218-9192-6
Product Code:  CBMS/116.E
List Price: $37.00
MAA Member Price: $33.30
AMS Member Price: $29.60
Softcover ISBN:  978-0-8218-8979-4
eBook: ISBN:  978-0-8218-9192-6
Product Code:  CBMS/116.B
List Price: $77.00 $58.50
Deformation Theory of Algebras and Their Diagrams
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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
Softcover ISBN:  978-0-8218-8979-4
Product Code:  CBMS/116
List Price: $40.00
Individual Price: $32.00
eBook ISBN:  978-0-8218-9192-6
Product Code:  CBMS/116.E
List Price: $37.00
MAA Member Price: $33.30
AMS Member Price: $29.60
Softcover ISBN:  978-0-8218-8979-4
eBook ISBN:  978-0-8218-9192-6
Product Code:  CBMS/116.B
List Price: $77.00 $58.50
  • Book Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 1162012; 129 pp
    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.

    Readership

    Graduate 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 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1162012; 129 pp
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.

Readership

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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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