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Noncommutative deformation theory / Eivind Eriksen, Olav Arnfinn Laudal, Arvid Siqveland

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Eriksen, Eivind [VerfasserIn]

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Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Monographs and research notes in mathematicsVerlag: Boca Raton : CRC Press, 2017Beschreibung: 1 Online-RessourceSchlagwörter:

Andere physische Formen: 149879601X | 9781498796019 | 1498796028. | 9781498796026. DDC-Klassifikation:

516.3/5

MSC: MSC: *14A22 | 14B12 | 14B07 | 14D20LOC-Klassifikation:

QA564

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Zusammenfassung: 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 functorsZusammenfassung: 3.3 Examples of noncommutative deformation functors3.3.1 Modules; 3.3.2 Modules with group action; 3.4 Noncommutative deformations of sheaves and presheaves; 3.4.1 Deformations of presheaves of modules; 3.4.2 Deformations of quasi-coherent sheaves of modules; 3.4.3 Quasi-coherent ringed schemes; 3.4.4 Calculations for D-modules on elliptic curves; 3.5 Matric Massey products and A-infinity structures; 3.5.1 Matric Massey products on differential graded algebras; 3.5.2 Matric Massey products and obstruction calculus; 3.5.3 Matric A-infinity algebras; 3.6 The Generalised Burnside TheoremZusammenfassung: 3.6.1 The algebra of observables3.6.2 The kernel of the miniversal morphism; 3.6.3 Iterated extensions and matric Massey products; 3.6.4 The Generalised Burnside Theorem; 3.6.5 Properties of the algebra of observables; 3.7 Iterated extension; 3.7.1 Moduli of iterated extensions; 3.7.2 The category of iterated extensions; 4 The Noncommutative Phase Space; 4.1 Introduction to noncommutative phase spaces; 4.1.1 The noncommutative Kodaira-Spencer map; 4.1.2 Generalised momenta; 4.2 The iterated phase space functor and the Dirac derivation; 4.2.1 The Dirac derivationZusammenfassung: 4.2.2 The generalised de Rham complex4.3 Differentiable structures on the moduli of representations; 4.3.1 Dynamical structures; 4.3.2 Representations of Ph[sup(∞)](A); 4.4 Gauge groups and invariant theory; 4.5 The generic dynamical structures associated to a metric; 4.5.1 The commutative case and general relativity; 4.5.2 The general case; 4.6 Classical gauge invariance and metric classification of representations; 4.6.1 The classical gauge invariance; 4.6.2 Chern characters and Chern-Simons classes; 4.6.3 A generalised Yang-Mills theory; 4.6.4 The classical Yang-Mills equationZusammenfassung: 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 theoryPPN: PPN: 1003132065Package identifier: Produktsigel: ZDB-4-NLEBK

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