Search Results - "Lie algebra"

Lie algebras, geometry and Toda-type systems by Razumov, Alexander V. (Alexander Vitalievich), 1952-

Subjects: “…Lie algebras.…”

Advances in geometry and lie algebras from supergravity by Frè, P.

Contents: “…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.…”
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Poisson structures and their normal forms by Dufour, Jean-Paul

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Differential geometry, Lie groups, and symmetric spaces by Helgason, Sigurdur, 1927-

Contents: “…Elementary Differential Geometry. Lie Groups and Lie Algebras. Structure of Semisimple Lie Algebras. Symmetric Spaces. …”
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Differential geometry and the calculus of variations by ScienceDirect (Online service)

Contents: “…Tangent vector-vector field formalism -- Differential forms -- Specialization to euclidean spaces : differential manifolds -- Mappings, submanifolds, and the implicit function theorem -- Jacobi bracket and the lie theory of ordinary differential equations -- Frobenius complete integrability theorem -- Reduction of dimension when a lie algebra of vector fields leaves a vector-fields invariant -- Lie groups -- Classical mechanics of particles and continua -- Differential forms and variational problems -- Hamilton-Jacobi theory -- Extremal fields and sufficient conditions for a minimum -- Ordinary problems of the calculus of variations -- Groups of symmetries of variational problems : applications to mechanics -- Elliptic functions -- Accessibility problems for path systems -- Affine connections on differential manifolds -- Rinmannian affine connection and the first variation formula -- Hopf-Rinow theorem applications to the theory of covering spaces -- Second variation formula and Jacobi vector fields -- Sectional curvature and the elementary comparision theorems -- Submanifolds of Riemannian manifolds -- Groups of isometries -- Deformation of submanifolds in Riemannian spaces -- First-order invariants of submanifolds and convexity for affinely connected manifolds -- Affine groups of automorphisms, induced connections on submanifolds, projective changes of connection -- Laplace-Beltrami operator -- Characteristics and shock waves -- Morse index theorem -- Complex manifolds and their submanifolds -- Mechanics on Riemannian manifolds.…”
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Differential geometry and mathematical physics. Part II, Fibre bundles, topology and gauge fields by Rudolph, Gerd, Schmidt, Matthias (Physicist)

Contents: “…Characteristic classes -- Clifford algebras, spin structures and Dirac operators -- The Yang-Mills equation -- Matter fields and model building -- The gauge orbit space -- Elements of quantum gauge theory -- A Field restriction and field extension -- B The Conformal Group of the 4-sphere -- C Simple Lie algebras. Root diagrams -- D z -function regularization -- E K-theory and index bundles -- F Determinant line bundles -- G Eilenberg-MacLane spaces -- References. …”
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Introduction to differential geometry by Robbin, Joel W.

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Differential geometry and Lie groups : a computational perspective by Gallier, Jean H., Quaintance, Jocelyn

Contents: “…Isometries, Submersions, Killing Vector Fields -- 18. Lie Groups, Lie Algebra, Exponential Map -- 19. The Derivative of exp and Dynkin's Formula ₎"-- 20. …”
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From geometry to quantum mechanics : in honor of Hideki Omori by SpringerLink (Online service)

Contents: “…Global Analysis and Infinite-Dimensional Lie Groups -- Aspects of Stochastic Global Analysis -- A Lie Group Structure for Automorphisms of a Contact Weyl Manifold -- Riemannian Geometry -- Projective Structures of a Curve in a Conformal Space -- Deformations of Surfaces Preserving Conformal or Similarity Invariants -- Global Structures of Compact Conformally Flat Semi-Symmetric Spaces of Dimension 3 and of Non-Constant Curvature -- Differential Geometry of Analytic Surfaces with Singularities -- Symplectic Geometry and Poisson Geometry -- The Integration Problem for Complex Lie Algebroids -- Reduction, Induction and Ricci Flat Symplectic Connections -- Local Lie Algebra Determines Base Manifold -- Lie Algebroids Associated with Deformed Schouten Bracket of 2-Vector Fields -- Parabolic Geometries Associated with Differential Equations of Finite Type -- Quantizations and Noncommutative Geometry -- Toward Geometric Quantum Theory -- Resonance Gyrons and Quantum Geometry -- A Secondary Invariant of Foliated Spaces and Type III? …”
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Dynamical systems and microphysics : geometry and mechanics : the proceedings of the 2nd International Seminar on Mathematical Theory of Dynamical Systems and Microphysics held at... by International Seminar on Mathematical Theory of Dynamical Systems and Microphysics Udine, Italy, ScienceDirect (Online service)

Contents: “…6 -- THE VEY STAR-PRODUCTS7 -- INTRODUCTION TO A SPECTRAL THEORY AND QUANTIZATION; 8 -- THE CASE WHERE b2(W) = 0; 9 -- LIE ALGEBRAS GENERATED BY A WEAK TWISTED PRODUCT AND VEY LIE ALGEBRAS; 10 -- EXISTENCE THEOREM; 11 -- INVARIANT STAR PRODUCTS; CHAPTER 3. …”
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Hermitian-Grassmannian submanifolds : Daegu, Korea, July 2016 by International Workshop on Hermitian Symmetric Spaces and Submanifolds Taegu, Korea, SpringerLink (Online service)

Contents: “…Constant mean curvature spacelike hypersurfaces in spacetimes with certain causal symmetries -- Sequences of maximal antipodal sets of oriented real Grassmann manifolds II -- Derivative on real hypersurfaces of non-flat complex space forms -- Maximal antipodal subgroups of the automorphism groups of compact Lie algebras -- A nearly K{\"a}hler submanifold with vertically pluri-harmonic lift -- The Schwarz lemma for super-conformal maps -- Reeb recurrent structure Jacobi operator on real hypersurfaces in complex two-plane Grassmannians -- Hamiltonian non-displaceability of the Gauss images of isoparametric hypersurfaces -- Counterexamples to Goldberg Conjecture with reversed orientation on Walker 8-manifolds of neutral signature -- A construction of weakly reflective submanifolds in compact symmetric spaces -- The dual Orlicz mixed Quermassintegral -- Characterizations of a Clifford hypersurface in a unit sphere -- 3-dimensional real hypersurfaces with $\eta$-harmonic curvature -- Gromov-Witten Invariants on the products of Almost Contact Metric Manifolds -- On LVMB, but not LVM, manifolds -- Inequalities for algebraic Casorati curvatures and their applications -- Volume-preserving mean curvature flow for tubes in rank one symmetric spaces of non-compact type -- A duality between compact symmetric triads and semisimple pseudo-Riemannian symmetric pairs with applications to geometry of Hermann type actions -- Transversally complex submanifolds of a quaternion projective space -- On Floer homology of the Gauss images of isoparametric hypersurfaces -- On the pointwise slant submanifolds -- Riemannian Hilbert manifolds -- Real hypersurfaces in Hermitian symmetric space of rank̃two with Killing shape operator -- The Chern-Moser-Tanaka invariant on pseudo-Hermitian almost CR manifolds -- Bott Periodicity, Submanifolds, and Vector Bundles -- The solvable models of noncompact real two-plane Grassmannians and some applications -- Biharmonic homogeneous submanifolds in compact symmetric spaces -- Recent results on real Hypersurfaces in Complex quadrics.…”
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Lie groups, geometry, and representation theory : a tribute to the life and work of Bertram Kostant by SpringerLink (Online service)

Contents: “…On Dimension Growth of Modular Irreducible Representations of Semisimple Lie Algebras1 Introduction; 2 Preliminaries; 2.1 Harish-Chandra bimodules and primitive ideals; 2.2 Hecke algebras, cells, and HC-bimodules; 2.3 Localization in characteristic p; 3 Lengths; 3.1 Reduction of HC-bimodules to characteristic p; 3.2 Results on growth of lengths; 3.3 Lengths for HC-bimodules; 3.4 Lengths in characteristic p; 4 Proof of Theorem 1.1; 4.1 Proof of part (1) of Theorem 1.1; 4.2 Outline of the proof of (2) of Theorem 1.1; 4.3 Etingof's construction; 4.4 Proof of Proposition 4.2; 4.5 Degeneration map.…”
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