1.
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The relation between the Jacobi morphism and the Hessian in gauge-natural field theories

Theoretical and Mathematical Physics, ISSN 0040-5779, 8/2007, Volume 152, Issue 2, pp. 1191 - 1200

We generalize a classic result, due to Goldschmidt and Sternberg, relating the Jacobi morphism and the Hessian for first-order field theories to higher-order gauge-natural field theories...

gauge-natural bundle | Mathematical and Computational Physics | jet | Applications of Mathematics | generalized Jacobi morphism | Physics | second variational derivative | Jet | Generalized Jacobi morphism | Second variational derivative | Gauge-natural bundle | LAGRANGIAN-FORMALISM | PHYSICS, MULTIDISCIPLINARY | VARIATIONAL SEQUENCES | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL

gauge-natural bundle | Mathematical and Computational Physics | jet | Applications of Mathematics | generalized Jacobi morphism | Physics | second variational derivative | Jet | Generalized Jacobi morphism | Second variational derivative | Gauge-natural bundle | LAGRANGIAN-FORMALISM | PHYSICS, MULTIDISCIPLINARY | VARIATIONAL SEQUENCES | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL

Journal Article

Archivum Mathematicum, ISSN 0044-8753, 2005, Volume 41, Issue 3, pp. 289 - 310

Journal Article

Reports on Mathematical Physics, ISSN 0034-4877, 2005, Volume 56, Issue 1, pp. 11 - 22

By resorting to Noether's Second Theorem, we relate the generalized Bianchi identities for Lagrangian field theories on gauge-natural bundles with the kernel of the associated gauge-natural Jacobi morphism...

generalized Bianchi identities | jets | gauge-natural bundles | generalized Jacobi morphisms | curvature | Gauge-natural bundles | Jets | Generalized Jacobi morphisms | Generalized Bianchi identities | Curvature | SEQUENCES | MORPHISMS | EQUATIONS | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL

generalized Bianchi identities | jets | gauge-natural bundles | generalized Jacobi morphisms | curvature | Gauge-natural bundles | Jets | Generalized Jacobi morphisms | Generalized Bianchi identities | Curvature | SEQUENCES | MORPHISMS | EQUATIONS | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL

Journal Article

Reports on Mathematical Physics, ISSN 0034-4877, 2004, Volume 54, Issue 3, pp. 349 - 364

.... Vice versa all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms which are in the kernel of generalized Jacobi morphisms are generators of canonical covariant currents and superpotentials...

invariant variational principles | gauge-natural bundles | variational sequences | conservation laws | generalized Jacobi morphisms | Conservation laws | Gauge-natural bundles | Invariant variational principles | Generalized Jacobi morphisms | Variational sequences | EINSTEIN | PHYSICS, MATHEMATICAL | GENERAL RELATIVITY | Environmental law

invariant variational principles | gauge-natural bundles | variational sequences | conservation laws | generalized Jacobi morphisms | Conservation laws | Gauge-natural bundles | Invariant variational principles | Generalized Jacobi morphisms | Variational sequences | EINSTEIN | PHYSICS, MATHEMATICAL | GENERAL RELATIVITY | Environmental law

Journal Article

Extracta mathematicae, ISSN 0213-8743, 2016, Volume 31, Issue 2, pp. 199 - 225

.... It is known that the base of a generalized Lie bialgebroid carries a Jacobi structure. In this paper, we introduce a notion of morphism between gen- eralized Lie...

coisotropic submanifolds | acobi manifolds | cobi groupoids | (generalized) Lie bialgebroids

coisotropic submanifolds | acobi manifolds | cobi groupoids | (generalized) Lie bialgebroids

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 07/2017, Volume 13

We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear...

Poisson structures | Symplectic structures | Contact structures | Jacobi structures | Lie groupoids | Principal bundles | Symplectic groupoids | symplectic structures | INTEGRABILITY | CLASSICAL PSEUDOGROUPS | QUANTUM | PHYSICS, MATHEMATICAL | ALGEBRAS | INTEGRATION | GROUPOIDS | GRADED BUNDLES | principal bundles | symplectic groupoids | GENERALIZED LIE BIALGEBROIDS | MANIFOLDS | contact structures | Bundling | Geometry | Programmable logic controllers | Manifolds (mathematics) | Bundles

Poisson structures | Symplectic structures | Contact structures | Jacobi structures | Lie groupoids | Principal bundles | Symplectic groupoids | symplectic structures | INTEGRABILITY | CLASSICAL PSEUDOGROUPS | QUANTUM | PHYSICS, MATHEMATICAL | ALGEBRAS | INTEGRATION | GROUPOIDS | GRADED BUNDLES | principal bundles | symplectic groupoids | GENERALIZED LIE BIALGEBROIDS | MANIFOLDS | contact structures | Bundling | Geometry | Programmable logic controllers | Manifolds (mathematics) | Bundles

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 4/1993, Volume 336, Issue 2, pp. 933 - 947

..., for by doing so we are able (a) to verify both the usual and generalized Hodge conjectures for Ã; (b) to describe both the kernel and the image of the Abel-Jacobi map from algebraic cycles algebraically equivalent to zero...

Morphisms | Integers | Tensors | Algebra | Mathematical theorems | Mathematical vectors | Jacobians | Family structure | Mathematical cusps | Generalized Hodge conjecture | Kuga variety | Cusp forms | Hodge conjecture | Tate conjecture | Elliptic curve | Abel-Jacobi map | Intermediate Jacobian | MATHEMATICS | ELLIPTIC CURVE | ABELIAN-VARIETIES | ABEL-JACOBI MAP | HODGE CONJECTURE | TATE CONJECTURE | GENERALIZED HODGE CONJECTURE | KUGA VARIETY | INTERMEDIATE JACOBIAN | CUSP FORMS

Morphisms | Integers | Tensors | Algebra | Mathematical theorems | Mathematical vectors | Jacobians | Family structure | Mathematical cusps | Generalized Hodge conjecture | Kuga variety | Cusp forms | Hodge conjecture | Tate conjecture | Elliptic curve | Abel-Jacobi map | Intermediate Jacobian | MATHEMATICS | ELLIPTIC CURVE | ABELIAN-VARIETIES | ABEL-JACOBI MAP | HODGE CONJECTURE | TATE CONJECTURE | GENERALIZED HODGE CONJECTURE | KUGA VARIETY | INTERMEDIATE JACOBIAN | CUSP FORMS

Journal Article

Annals of Global Analysis and Geometry, ISSN 0232-704X, 9/2019, Volume 56, Issue 2, pp. 221 - 244

A Jacobi structure J on a line bundle $$L\rightarrow M$$ L → M is weakly regular, if the sharp map $$J^\sharp : J^1 L \rightarrow DL$$ J ♯ : J 1 L...

Geometry | Mathematical Physics | Analysis | Global Analysis and Analysis on Manifolds | Mathematics | Contact geometry | Differential Geometry | Generalized complex geometry | Differential geometry | MATHEMATICS | ALGEBRAS | Bundling | Bundles

Geometry | Mathematical Physics | Analysis | Global Analysis and Analysis on Manifolds | Mathematics | Contact geometry | Differential Geometry | Generalized complex geometry | Differential geometry | MATHEMATICS | ALGEBRAS | Bundling | Bundles

Journal Article

Experimental Mathematics, ISSN 1058-6458, 04/2015, Volume 24, Issue 2, pp. 247 - 259

For motives associated with Fermat curves, there are elements in motivic cohomology whose regulators are written in terms of special values of generalized...

regulator | L-function | hypergeometric function | MATHEMATICS | ABELIAN INTEGRALS | GENERALIZED HYPERGEOMETRIC-FUNCTIONS | PERIODS | FERMAT-CURVES

regulator | L-function | hypergeometric function | MATHEMATICS | ABELIAN INTEGRALS | GENERALIZED HYPERGEOMETRIC-FUNCTIONS | PERIODS | FERMAT-CURVES

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 5/2007, Volume 80, Issue 2, pp. 155 - 169

We study quasi-Jacobi and Jacobi-quasi bialgebroids and their relationships with twisted Jacobi and quasi Jacobi manifolds...

quasi-Jacobi bialgebroid | Mathematical and Computational Physics | 53D10 | quasi-Jacobi bialgebra | Physics | 53D17 | Geometry | 17B66 | 17B62 | Jacobi-quasi bialgebroid | Group Theory and Generalizations | twisted Jacobi manifold | Statistical Physics | quasi Jacobi manifold | Quasi-Jacobi bialgebra | Twisted Jacobi manifold | Quasi-Jacobi bialgebroid | Quasi Jacobi manifold | GENERALIZED LIE BIALGEBROIDS | POISSON MANIFOLDS | PHYSICS, MATHEMATICAL

quasi-Jacobi bialgebroid | Mathematical and Computational Physics | 53D10 | quasi-Jacobi bialgebra | Physics | 53D17 | Geometry | 17B66 | 17B62 | Jacobi-quasi bialgebroid | Group Theory and Generalizations | twisted Jacobi manifold | Statistical Physics | quasi Jacobi manifold | Quasi-Jacobi bialgebra | Twisted Jacobi manifold | Quasi-Jacobi bialgebroid | Quasi Jacobi manifold | GENERALIZED LIE BIALGEBROIDS | POISSON MANIFOLDS | PHYSICS, MATHEMATICAL

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 03/2019, Volume 16, Issue 3

... gauge-natural Jacobi morphism.

reduced principal bundle | classical Higgs field | reduced Lie algebra | Yang-Mills Lagrangian | Cartan connection | GENERALIZED BIANCHI IDENTITIES | INVARIANT VARIATIONAL-PROBLEMS | CONNECTIONS | PHYSICS, MATHEMATICAL | GEOMETRY

reduced principal bundle | classical Higgs field | reduced Lie algebra | Yang-Mills Lagrangian | Cartan connection | GENERALIZED BIANCHI IDENTITIES | INVARIANT VARIATIONAL-PROBLEMS | CONNECTIONS | PHYSICS, MATHEMATICAL | GEOMETRY

Journal Article

12.
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Twisted Jacobi manifolds, twisted Dirac–Jacobi structures and quasi-Jacobi bialgebroids

Journal of Physics A: Mathematical and General, ISSN 0305-4470, 08/2006, Volume 39, Issue 33, pp. 10449 - 10475

We study twisted Jacobi manifolds, a concept that we had introduced in a previous note...

GENERALIZED LIE BIALGEBROIDS | POISSON MANIFOLDS | ALGEBRAS | PHYSICS, MATHEMATICAL

GENERALIZED LIE BIALGEBROIDS | POISSON MANIFOLDS | ALGEBRAS | PHYSICS, MATHEMATICAL

Journal Article

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, ISSN 1578-7303, 3/2012, Volume 106, Issue 1, pp. 191 - 224

...–Jacobi theory and integrability characterizations, and the construction of suitable geometric integrators...

70H20 | 70H33 | Nonholonomic mechanics | Theoretical, Mathematical and Computational Physics | Geometric integrators | 37J60 | Mathematics, general | Mathematics | Applications of Mathematics | Symmetries and reduction | Hamilton–Jacobi theory | 70F25 | Hamilton-Jacobi theory | VARIATIONAL-PRINCIPLES | GEOMETRICAL FRAMEWORK | FACTORIZATION | CONSTRAINT ALGORITHM | NONHOLONOMIC LAGRANGIAN SYSTEMS | EQUATIONS | FORMULATION | MATHEMATICS | GENERALIZED HAMILTONIAN-DYNAMICS | ALMOST-POISSON STRUCTURES | INTEGRATORS

70H20 | 70H33 | Nonholonomic mechanics | Theoretical, Mathematical and Computational Physics | Geometric integrators | 37J60 | Mathematics, general | Mathematics | Applications of Mathematics | Symmetries and reduction | Hamilton–Jacobi theory | 70F25 | Hamilton-Jacobi theory | VARIATIONAL-PRINCIPLES | GEOMETRICAL FRAMEWORK | FACTORIZATION | CONSTRAINT ALGORITHM | NONHOLONOMIC LAGRANGIAN SYSTEMS | EQUATIONS | FORMULATION | MATHEMATICS | GENERALIZED HAMILTONIAN-DYNAMICS | ALMOST-POISSON STRUCTURES | INTEGRATORS

Journal Article

Journal of Physics A: Mathematical and General, ISSN 0305-4470, 04/2006, Volume 39, Issue 16, pp. 4181 - 4190

We study precontact groupoids whose infinitesimal counterparts are Dirac-Jacobi structures...

BRACKETS | ALGEBRAS | PHYSICS, MULTIDISCIPLINARY | GROUPOIDS | GENERALIZED LIE BIALGEBROIDS | MANIFOLDS | PHYSICS, MATHEMATICAL

BRACKETS | ALGEBRAS | PHYSICS, MULTIDISCIPLINARY | GROUPOIDS | GENERALIZED LIE BIALGEBROIDS | MANIFOLDS | PHYSICS, MATHEMATICAL

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2007, Volume 359, Issue 1, pp. 1 - 17

.... Here~n is the dimension of X, while b is its first Betti number. The proof of the inequalities involves constructing Abel-Jacobi maps from X to its Jacobi torus~\mathbb...

Geometry | Riemann manifold | Mathematical theorems | Mathematical lattices | Linear transformations | Mathematical constants | Mathematical inequalities | Systole | Vector spaces | Ellipsoids | Conformal systole | Generalized degree | Lp-minimizing differential forms | Perfect lattice | John ellipsoid | Loewner inequality | Deformation theorem | Extremal lattice | Isoperimetric inequality | Abel-Jacobi map | Free abelian cover | Riemannian submersion | generalized degree | perfect lattice | systolic inequality | FORMS | MATHEMATICS | stable systole | L-p-minimizing differential forms | REGULARITY | extremal lattice | conformal systole | isoperimetric inequality | free abelian cover | deformation theorem | SURFACES

Geometry | Riemann manifold | Mathematical theorems | Mathematical lattices | Linear transformations | Mathematical constants | Mathematical inequalities | Systole | Vector spaces | Ellipsoids | Conformal systole | Generalized degree | Lp-minimizing differential forms | Perfect lattice | John ellipsoid | Loewner inequality | Deformation theorem | Extremal lattice | Isoperimetric inequality | Abel-Jacobi map | Free abelian cover | Riemannian submersion | generalized degree | perfect lattice | systolic inequality | FORMS | MATHEMATICS | stable systole | L-p-minimizing differential forms | REGULARITY | extremal lattice | conformal systole | isoperimetric inequality | free abelian cover | deformation theorem | SURFACES

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 9/1997, Volume 7, Issue 3, pp. 387 - 435

All three subjects reflected in the title are closely intertwined in the paper.LetJ E be a class of Jacobi matrices acting inl 2(ℤ...

Character-automorphic functions | Mathematics | Almost periodic Jacobi matrices | Widom type Fuchsian groups | Generalized Abel map | 30F35 | Abstract Harmonic Analysis | Fourier Analysis | 47B39 | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Jacobi inversion | Differential Geometry | Dynamical Systems and Ergodic Theory

Character-automorphic functions | Mathematics | Almost periodic Jacobi matrices | Widom type Fuchsian groups | Generalized Abel map | 30F35 | Abstract Harmonic Analysis | Fourier Analysis | 47B39 | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Jacobi inversion | Differential Geometry | Dynamical Systems and Ergodic Theory

Journal Article

2004, ISBN 9812388516, xxii, 150

Book

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 2008, Volume 5, Issue 6, pp. 973 - 988

We investigate canonical aspects concerning the relation between symmetries and conservation laws in gauge-natural field theories. In particular, we find that...

Connections | Gauge-natural bundles | Jets | GENERALIZED BIANCHI IDENTITIES | CALCULUS | gauge-natural bundles | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | connections | RELATIVITY

Connections | Gauge-natural bundles | Jets | GENERALIZED BIANCHI IDENTITIES | CALCULUS | gauge-natural bundles | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | connections | RELATIVITY

Journal Article

JOURNAL OF GEOMETRIC MECHANICS, ISSN 1941-4889, 03/2009, Volume 1, Issue 1, pp. 1 - 34

.... Algebroids are, roughly speaking, vector bundles equipped with a bilinear bracket of sections and two vector bundle morphisms (the anchors maps...

MATHEMATICS, APPLIED | POISSON | Algebroids | CONNECTIONS | PHYSICS, MATHEMATICAL | nonholonomic mechanics | closed symplectic sections | gradient extension | REDUCTION | DIRAC STRUCTURES | DYNAMICS | Hamiltonian mechanics | LIFTS | SYSTEMS | exact symplectic algebroid | generalized nonholonomic systems | MANIFOLD

MATHEMATICS, APPLIED | POISSON | Algebroids | CONNECTIONS | PHYSICS, MATHEMATICAL | nonholonomic mechanics | closed symplectic sections | gradient extension | REDUCTION | DIRAC STRUCTURES | DYNAMICS | Hamiltonian mechanics | LIFTS | SYSTEMS | exact symplectic algebroid | generalized nonholonomic systems | MANIFOLD

Journal Article

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Action of correspondences on filtrations on cohomology and 0-cycles of Abelian varieties

Mathematische Zeitschrift, ISSN 0025-5874, 6/2019, Volume 292, Issue 1, pp. 655 - 675

....) that vanishes as a morphism on a certain quotient of its middle singular cohomology, then it vanishes as a morphism on the deepest part of a particular filtration on the Chow group of 0-cycles of the abelian variety...

Motives | Algebraic cycles | Generalized Kummer varieties | Abelian varieties | Bloch-Beilinson filtration | Mathematics, general | Mathematics | Chow groups | MATHEMATICS | CHOW | ALGEBRAIC CYCLES | K3 SURFACES | ZERO-CYCLES

Motives | Algebraic cycles | Generalized Kummer varieties | Abelian varieties | Bloch-Beilinson filtration | Mathematics, general | Mathematics | Chow groups | MATHEMATICS | CHOW | ALGEBRAIC CYCLES | K3 SURFACES | ZERO-CYCLES

Journal Article

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