Fourier Analysis -- Fourier Series -- Hilbert Spaces -- The Fourier Transform -- Distributions -- LCA Groups -- Finite Abelian Groups -- LCA Groups -- The Dual Group -- Plancherel Theorem -- Noncommutative Groups -- Matrix Groups -- The Representations of SU(2) -- The Peter-Weyl Theorem -- The Heisenberg Group.From the reviews of the first edition: "This lovely book is intended as a primer in h…
Curvature of Contact Metric Manifolds -- A Case for Curvature: the Unit Tangent Bundle -- Convex Hypersurfaces in Hadamard Manifolds -- Contact Metric Geometry of the Unit Tangent Sphere Bundle -- Topological-antitopological Fusion Equations, Pluriharmonic Maps and Special Kähler Manifolds -- ?2 and ?-Deformation Theory for Holomorphic and Symplectic Manifolds -- Commutative Condition on the S…
I -- The basics -- Bruhat order -- Weak order and reduced words -- Roots, games, and automata -- II -- Kazhdan-Lusztig and R-polynomials -- Kazhdan-Lusztig representations -- Enumeration -- Combinatorial Descriptions.Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxete…
Dirac structures, momentum maps, and quasi-Poisson manifolds -- Construction of Ricci-type connections by reduction and induction -- A mathematical model for geomagnetic reversals -- Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization -- Thompson’s conjecture for real semisimple Lie groups -- The Weinstein conjecture and theorems of nearby and almost exist…
What is Algebra? -- Fields -- Commutative Rings -- Homomorphisms and Ideals -- Modules -- Algebraic Aspects of Dimension -- The Algebraic View of Infinitesimal Notions -- Noncommutative Rings -- Modules over Noncommutative Rings -- Semisimple Modules and Rings -- Division Algebras of Finite Rank -- The Notion of a Group -- Examples of Groups: Finite Groups -- Examples of Groups: Infinite Discre…
Noncommutative Geometry -- Poisson Geometry and Deformation Quantization -- Applications in Physics -- Topological Quantum Field Theory.This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challeng…
1 Relativity based on symmetry -- 1.1 Space-time transformation based on relativity -- 1.2 Step 6 - Identification of invariants -- 1.3 Relativistic velocity addition -- 1.4 Step 7 - The velocity ball as a bounded symmetric domain -- 1.5 Step 8 - Relativistic dynamics -- 1.6 Notes -- 2 The real spin domain -- 2.1 Symmetric velocity addition -- 2.2 Projective and conformal commutativity and asso…
Part I: Modeling of mechanical systems; Introductory examples and problems; Linear and multilinear algebra; Differential geometry; Simple mechanical control systems; Lie groups, systems on groups, and symmetries -- Part II: Analysis of mechanical control systems; Stability; Controllability; Low-order controllability and kinematic reduction ; Perturbation analysis -- Part III: A sampling of desi…