Advances in geometry and lie algebras from supergravity. ([2018])

• Record Type: Book
• Further Information: Note: Pietro Giuseppe Fré.
• Authors: Frè, P
• Contents: Intro; Preface; Acknowledgements; Contents; 1 Finite Groups and Lie Algebras: The ADE Classification and Beyond; 1.1 The ADE Classification of the Finite Subgroups of SU(2); 1.1.1 The Argument Leading to the Diophantine Equation; 1.1.2 Case r=2: The Infinite Series of Cyclic Groups mathfrakan; 1.1.3 Case r=3 and its Solutions; 1.1.4 Summary of the ADE Classification of Finite Rotation Groups; 1.2 Lattices and Crystallographic Groups; 1.2.1 Lattices; 1.2.2 Crystallographic Groups and the Bravais Lattices for n=3; 1.2.3 The Proper Point Groups; 1.2.4 The Cubic Lattice and Its Point Group. 1.2.5 The Octahedral Group O24simS41.2.6 Irreducible Representations of the Octahedral Group; 1.3 A Simple Crystallographic Point-Group in 7-Dimensions; 1.3.1 The Simple Group L168; 1.3.2 Structure of the Simple Group L168=PSL(2, mathbbZ7); 1.3.3 The 7-Dimensional Irreducible Representation; 1.3.4 The 3-Dimensional Complex Representations; 1.3.5 The 6-Dimensional Representation; 1.3.6 The 8-Dimensional Representation; 1.3.7 The Proper Subgroups of L168; 1.4 The General Form of a Simple Lie Algebra and the Root Systems; 1.4.1 The Cartan Matrices; 1.4.2 Dynkin Diagrams. 1.5 The Classification Theorem1.6 The Exceptional Lie Algebra mathfrakg2; 1.7 A Golden Splitting for Quaternionic Algebras; 1.7.1 The Golden Splitting of the Quaternionic Algebra mathfrakg2; 1.7.2 Chevalley-Serre Basis; 1.8 The Lie Algebra mathfrakf4 and its Fundamental Representation; 1.8.1 Explicit Construction of the Fundamental and Adjoint Representation of mathfrakf4; 1.9 Conclusions for This Chapter; References; 2 Isometries and the Geometry of Coset Manifolds; 2.1 Conceptual and Historical Introduction; 2.1.1 Symmetric Spaces and Elie Cartan. 2.1.2 Where and How Do Coset Manifolds Come into Play?2.1.3 The Deep Insight of Supersymmetry; 2.2 Isometries and Killing Vector Fields; 2.3 Coset Manifolds; 2.3.1 The Geometry of Coset Manifolds; 2.4 The Real Sections of a Complex Lie Algebra and Symmetric Spaces; 2.5 The Solvable Group Representation of Non-compact Coset Manifolds; 2.5.1 The Tits Satake Projection: An Anticipation; References; 3 Complex and Quaternionic Geometry; 3.1 Imaginary Units and Geometry; 3.1.1 The Precognitions of Supersymmetry; 3.2 Complex Structures on 2n-Dimensional Manifolds. 3.3 Metric and Connections on Holomorphic Vector Bundles3.4 Characteristic Classes and Elliptic Complexes; 3.5 KÃÞhler Metrics; 3.6 Hypergeometry; 3.6.1 Quaternionic KÃÞhler, Versus HyperKÃÞhler Manifolds; 3.7 Moment Maps; 3.7.1 The Holomorphic Moment Map on KÃÞhler Manifolds; 3.7.2 The Triholomorphic Moment Map on Quaternionic Manifolds; 3.8 KÃÞhler Surfaces with One Continuous Isometry; 3.8.1 The Curvature and the KÃÞhler Potential of the Surface Σ; 3.8.2 Asymptotically Flat KÃÞhler Surfaces with an Elliptic Isometry Group.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Copyright Date: 2018
• Extent: 1 online resource (xx, 556 pages), illustrations (some color)
• Subjects: 516.3/6; Physics; Geometry, Differential; Lie algebras; MATHEMATICS -- Geometry -- General; Geometry, Differential; Lie algebras; Science -- Physics; Mathematics -- Geometry -- Differential; Science -- Mathematical Physics; History of science; Differential & Riemannian geometry; Mathematical physics; Quantum theory; Global differential geometry; Science -- Nuclear Physics; Quantum physics (quantum mechanics & quantum field theory); Electronic books
• Languages: English
• ISBNs: 9783319744919; 3319744917
• Related ISBNs: 9783319744902; 3319744909
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed February 27, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.