**CBMS Regional Conference Series in Mathematics**

Volume: 116;
2012;
129 pp;
Softcover

MSC: Primary 13; 14;
Secondary 53; 55

Print ISBN: 978-0-8218-8979-4

Product Code: CBMS/116

List Price: $35.00

Individual Price: $28.00

**Electronic ISBN: 978-0-8218-9192-6
Product Code: CBMS/116.E**

List Price: $35.00

Individual Member Price: $28.00

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#### Supplemental Materials

# Deformation Theory of Algebras and Their Diagrams

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*Martin Markl*

A co-publication of the AMS and CBMS

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.

#### Table of Contents

# Table of Contents

## Deformation Theory of Algebras and Their Diagrams

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- Basic notions 112 free
- Deformations and cohomology 1930
- Finer structures of cohomology 2536
- The gauge group 4556
- The simplicial Maurer-Cartan space 5566
- Strongly homotopy Lie algebras 6980
- Homotopy invariance and quantization 7586
- Brief introduction to operads 8596
- 𝐿_{∞}-algebras governing deformations 99110
- Examples 113124
- Index 121132 free
- Bibliography 125136
- Back Cover Back Cover1143

#### Readership

Graduate students and research mathematicians interested in deformations of algebras, moduli spaces, algebraic geometry, and/or algebraic topology.