Search Results - "Lie algebra"
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Lie algebras, geometry and Toda-type systems
Published: Cambridge University Press, 1997Subjects: “…Lie algebras.…”Description: xix, 247 pages ; 23 cm.
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Advances in geometry and lie algebras from supergravity
Published: Springer, 2018Contents: “…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.…”Description: 1 online resource (xx, 556 pages) : illustrations (some color).
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Poisson structures and their normal forms
Published: Birkhäuser Verlag, 2005Subjects: SpringerLink - Click here for accessDescription: 1 online resource (xv, 321 pages) : illustrations.
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Differential geometry, Lie groups, and symmetric spaces
Published: Academic Press, 1978Contents: “…Elementary Differential Geometry. Lie Groups and Lie Algebras. Structure of Semisimple Lie Algebras. Symmetric Spaces. …”Description: 1 online resource (xv, 628 pages).
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Differential geometry and the calculus of variations
Published: Elsevier Science, 1968Contents: “…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.…”Description: 1 online resource (vii, 440 pages).
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Differential geometry and mathematical physics. Part II, Fibre bundles, topology and gauge fields
Published: Springer, 2017Contents: “…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. …”Description: 1 online resource.
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Introduction to differential geometry
Published: Springer, 2022SpringerLink - Click here for accessDescription: 1 online resource.
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Differential geometry and Lie groups : a computational perspective
Published: Springer, 2020Contents: “…Isometries, Submersions, Killing Vector Fields -- 18. Lie Groups, Lie Algebra, Exponential Map -- 19. The Derivative of exp and Dynkin's Formula ₎"-- 20. …”Description: 1 online resource.
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From geometry to quantum mechanics : in honor of Hideki Omori
Published: Birkhäuser, 2007Contents: “…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? …”Description: 1 online resource (xvii, 324 pages) : illustrations.
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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...
Published: Academic Press, 1982Contents: “…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. …”Description: 1 online resource (xiii, 465 pages) : illustrations.
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Hermitian-Grassmannian submanifolds : Daegu, Korea, July 2016
Published: Springer, 2017Contents: “…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.…”Description: 1 online resource (xi, 360 pages).
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Lie groups, geometry, and representation theory : a tribute to the life and work of Bertram Kostant
Published: Birkhäuser, 2018Contents: “…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.…”Description: 1 online resource.
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