Noncommutative deformation theory
"Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry. This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative algebras and to quantum theory in physics. An essential part of this theory is the study of obstructions of liftings of representations using generalised (matric) Massey products. Suitable for research…
Read More ↓Title Statements
- Full title :Noncommutative deformation theory / Eivind Eriksen, Olav Arnfinn Laudal, Arvid Siqveland.
Summary
"Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry. This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative algebras and to quantum theory in physics. An essential part of this theory is the study of obstructions of liftings of representations using generalised (matric) Massey products. Suitable for researchers in algebraic geometry and mathematical physics interested in the workings of noncommutative algebraic geometry, it may also be useful for advanced graduate students in these fields."--Provided by publisher.
Read More ↓Edition Statements
- Publication Date:©20
Publication Statements
- Publisher(s):CRC Press
- Place of Publication:Boca Raton
- Language:eng
- Publication Date:©20
The Physical Object
- Description:1 online resource
Edition Identifiers
- ISBN:9781498796026, 1498796028, 1315156059, 9781315156057, 1351652125, 9781351652124
- oclc:ocn987580968
- LC Classification:QA564
- Dewey Decimal:516.3/5
Table of Contents
Cover; Half Title; Title Page; Copyright Page; Contents; Introduction; How to Read This Book; 1 Classical Deformation Theory; 1.1 General principles; 1.2 Formal deformations and infinitesimal deformations; 1.3 Functors of Artin rings; 1.3.1 Tangent spaces; 1.3.2 Obstruction calculus; 1.4 Deformations of associative algebras; 1.4.1 Tangent space and obstruction calculus; 1.4.2 Examples; 1.5 Deformations of modules; 1.5.1 Tangent space and obstruction calculus; 1.5.2 Examples; 2 Noncommutative Algebras and Simple Modules; 2.1 Noncommutative algebras; 2.2 Artin-Wedderburn theory.
2.3 Simple modules and the Jacobson radical2.4 The classical theorems of Burnside, Wedderburn, and Malcev; 2.5 Finite dimensional simple modules; 3 Noncommutative Deformation Theory; 3.1 Noncommutative deformation functors; 3.1.1 Flatness in Abelian categories; 3.1.2 Commutative deformation functors; 3.1.3 Noncommutative deformation functors; 3.2 Structure of noncommutative deformation functors; 3.2.1 Functors of noncommutative Artin rings; 3.2.2 Algebraizations; 3.2.3 Tangent spaces; 3.2.4 Obstruction calculus; 3.2.5 Swarms; 3.2.6 Relations with commutative deformation functors.
3.3 Examples of noncommuta…
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