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Pacific journal of mathematics, ISSN 0030-8730, 2016, Volume 283, Issue 2, pp. 449 - 482
.... A particularly relevant class of structures consists of vector bundle valued differential forms... 
Lie algebroids | Graded manifolds | Spencer operators | NQ-manifolds | Vector bundle valued differential forms | MATHEMATICS | graded manifolds | JACOBI STRUCTURES | vector bundle valued differential forms | GEOMETRY
Journal Article
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, ISSN 1815-0659, 2018, Volume 14
.... Our ideas are based on a description of (Lie) algebroids as vector bundle comorphisms - differential relations of a special kind... 
CLASSICAL PSEUDOGROUPS | QUANTUM | PHYSICS, MATHEMATICAL | almost-Lie algebroid | variational principle | graded bundle | LAGRANGIAN SUBMANIFOLDS | MECHANICS | graded manifold | higher algebroid | vector bundle comorphism | GRADED BUNDLES | DYNAMICS | Q-MANIFOLDS | DUALITY | VARIATIONAL-PROBLEMS | algebroid lift | Bundling | Axioms
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 06/2018, pp. 1 - 51
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 09/2018, Volume 2018, Issue 17, pp. 5347 - 5377
Abstract We give a new method to construct linear spaces of matrices of constant rank, based on truncated graded cohomology modules of certain vector bundles as well as on the existence of graded... 
BETTI-NUMBERS | MATHEMATICS | COHOMOLOGY | SPACES | MONADS | INSTANTON BUNDLES | SYMMETRIC-MATRICES | CONSTANT RANK | Algebraic Geometry | Commutative Algebra | Mathematics
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 2/2019, Volume 109, Issue 2, pp. 243 - 293
Vector bundles and double vector bundles, or twofold vector bundles, arise naturally for instance as base spaces for algebraic structures such as Lie algebroids, Courant algebroids and double Lie algebroids... 
Geometry | Double vector bundle | 32C11 | Theoretical, Mathematical and Computational Physics | Complex Systems | Lie algebroid | Graded manifold | Group Theory and Generalizations | 51P05 | Physics | 53D17
Journal Article
Journal of geometry and physics, ISSN 0393-0440, 2009, Volume 59, Issue 9, pp. 1285 - 1305
A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F... 
Lie bialgebroids | Courant algebroids | Drinfeld doubles | BRST formalism | Double vector bundles | Graded super-manifolds | LEGENDRE TRANSFORMATION | 2ND-ORDER GEOMETRY | TANGENT | POISSON GROUPOIDS | PHYSICS, MATHEMATICAL | BIALGEBROIDS | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DUALITY | LIFTS | Mathematics - Differential Geometry
Journal Article
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 12/2018, Volume 15, Issue 12
We develop the concept of a double (more generally n-tuple) principal bundle departing from a compatibility condition for a principal action of a Lie group... 
Principal bundle | Lie groupoid | double vector bundles | group actions | DOUBLE LIE ALGEBROIDS | GRADED BUNDLES | PHYSICS, MATHEMATICAL
Journal Article
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 11/2016, Volume 12
... (a particular kind of graded manifold) and produces a k-fold vector bundle. We fully characterise the image of the full linearisation functor and show that we obtain... 
Polarisation | Supermanifolds | N-manifolds | Graded manifolds | K-fold vector bundles | supermani-folds | k-fold vector bundles | HIGHER-ORDER | POISSON | polarisation | LIE ALGEBROIDS | graded manifolds | Q-MANIFOLDS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 03/2016, Volume 101, pp. 71 - 99
Graded bundles are a class of graded manifolds which represent a natural generalisation of vector bundles and include the higher order tangent bundles as canonical examples... 
Poisson structures | Vector bundles | Lie algebroids | Lie groupoids | Graded manifolds | MATHEMATICS | MECHANICS | Q-MANIFOLDS | PHYSICS, MATHEMATICAL
Journal Article
LETTERS IN MATHEMATICAL PHYSICS, ISSN 0377-9017, 02/2019, Volume 109, Issue 2, pp. 243 - 293
Vector bundles and double vector bundles, or twofold vector bundles, arise naturally for instance as base spaces for algebraic structures such as Lie algebroids, Courant algebroids and double Lie algebroids... 
Double vector bundle | Lie algebroid | Graded manifold | PHYSICS, MATHEMATICAL
Journal Article
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 2018, Volume 16, Issue 2
Graded bundles are a particularly nice class of graded manifolds and represent a natural generalization of vector bundles... 
Lie algebroids | Graded bundles | actions | connections | double vector bundles | BUNDLES | MECHANICAL SYSTEMS | CATEGORY | PHYSICS, MATHEMATICAL
Journal Article
Compositio mathematica, ISSN 0010-437X, 12/2016, Volume 152, Issue 12, pp. 2545 - 2562
.... We apply this construction to Boij–Söderberg decompositions of cohomology tables of vector bundles, yielding a proof of concept for the idea that those positive... 
Boij-Söderberg theory | Sheaf cohomology | monads | BETTI-NUMBERS | MATHEMATICS | COHOMOLOGY | MULTIPLICITY CONJECTURE | FREE RESOLUTIONS | GRADED MODULES | Boij-Soderberg theory | VECTOR-BUNDLES | Theoretical mathematics | Construction | Mathematical analysis | Collection | Tables | Decomposition | Vectors (mathematics) | Bundles
Journal Article
Indagationes Mathematicae, ISSN 0019-3577, 2008, Volume 19, Issue 3, pp. 401 - 410
We prove, in an elementary way, that a locally free sheaf of finite rank over the anisotropic real conic is the direct sum of indecomposable locally free... 
Group action | Vector bundle | Twisted group ring | Locally free sheaf | Anisotropic real conic | Graded twisted group ring | Indecomposable vector bundle | Graded module | Indecomposable locally free sheaf | MATHEMATICS | CLASSIFICATION | Anisotropy
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 08/2016, Volume 47, pp. 212 - 245
Smooth actions of the multiplicative monoid (R,⋅) of real numbers on manifolds lead to an alternative, and for some reasons simpler, definitions of a vector bundle, a double vector bundle and related structures like a graded bundle... 
Homogeneity structure | Graded manifold | Monoid action | Graded bundle | Holomorphic bundle | Supermanifold | MATHEMATICS | MATHEMATICS, APPLIED | Manifolds | Bundling | Maps | Mathematical analysis | Jets | Vectors (mathematics) | Manifolds (mathematics) | Monoids | Mathematics - Differential Geometry
Journal Article
COMMUNICATIONS IN NUMBER THEORY AND PHYSICS, ISSN 1931-4523, 2019, Volume 13, Issue 3, pp. 487 - 528
... compactified modular curve, and we study their structure by relating it to the structure of vector bundles over orbifold curves of genus zero... 
MATHEMATICS | MATHEMATICS, APPLIED | Modular forms | REPRESENTATION-THEORY | graded modules | orbifold curves | PHYSICS, MATHEMATICAL | Fuchsian groups
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 2012, Volume 62, Issue 1, pp. 21 - 36
We introduce the concept of a graded bundle which is a natural generalization of the concept of a vector bundle and whose standard examples are higher tangent bundles T n Q playing a fundamental role... 
[formula omitted]-manifolds | Fiber bundles | Graded manifolds | Homogeneous functions | N-manifolds | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Mathematics - Differential Geometry
Journal Article
Indagationes Mathematicae, ISSN 0019-3577, 10/2014, Volume 25, Issue 5, pp. 1122 - 1134
We establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaĭntrob’s Lie algebroid... 
Representation up to homotopy | Q-manifold | Graded manifold | Graded vector bundle | Lie algebroid | MATHEMATICS | BRACKETS | COHOMOLOGY | DEFORMATIONS | Mathematics - Differential Geometry
Journal Article
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 01/2018, Volume 15, Issue 1
.... We also present the notion of double filtered bundles which provide natural generalisations of double vector bundles and double affine bundles... 
filtered rings | graded manifolds | Fiber bundles | jet manifolds | affine bundles
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 05/2015, Volume 48, Issue 20, pp. 1 - 32
In this paper we develop a geometric approach to higher order mechanics on graded bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered weighted algebroids... 
Higher order Lagrangians | Tulczyjew triple | Graded bundle | Geometrical mechanics | graded bundle | higher order Lagrangians | AV-DIFFERENTIAL GEOMETRY | POISSON | PHYSICS, MULTIDISCIPLINARY | LIE ALGEBROIDS | MANIFOLDS | PHYSICS, MATHEMATICAL | geometrical mechanics | LAGRANGIAN MECHANICS | Euler-Lagrange equation | Mathematical analysis | Formalism | Invariants | Bundles
Journal Article
Compositio mathematica, ISSN 0010-437X, 08/2015, Volume 151, Issue 8, pp. 1499 - 1528
.... We apply this to local systems, vector bundles, Higgs bundles, and representations of fundamental groups... 
cohomology jump locus | deformation theory | differential graded Lie algebra | local system | MATHEMATICS | MODULI SPACE | Algebra | Deformation | Mathematical analysis | Lie groups | Representations | Vectors (mathematics) | Loci | Bundles | Mathematics - Algebraic Geometry
Journal Article
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