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Advances in Mathematics, ISSN 0001-8708, 02/2016, Volume 290, pp. 163 - 207
We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids... 
Poisson groupoids | VB-algebroids | Double Lie algebroids | VB-groupoids | LA-groupoids | BRACKETS | INTEGRABILITY | REPRESENTATIONS | 2ND-ORDER GEOMETRY | HOMOTOPY | BIALGEBROIDS | MATHEMATICS | INTEGRATION | DUALITY
Journal Article
数学学报:英文版, ISSN 1439-8516, 2014, Volume 30, Issue 10, pp. 1655 - 1673
In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles... 
向量丛 | 短序列 | 对偶理论 | 操作 | jet bundles | Double vector bundles | 17B65 | Mathematics, general | Mathematics | 18B40 | DVB sequences | duality | 58H05 | MATHEMATICS | MATHEMATICS, APPLIED | LIE ALGEBROIDS | GEOMETRY | Studies | Theorems | Mathematical models | Algebra | Applied mathematics | Sequences | Construction | Equivalence | Categories | Mathematical analysis | Vectors (mathematics) | Bundles
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 01/2019, Volume 109, Issue 1, pp. 135 - 185
A triple vector bundle is a cube of vector bundle structures which commute in the (strict) categorical sense. A grid in a triple vector bundle is a collection of sections of each bundle structure with certain linearity properties... 
Connections | Double vector bundles | Curvature | Triple vector bundles | PHYSICS, MATHEMATICAL
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 06/2018, pp. 1 - 51
Journal Article
Comptes rendus - Mathématique, ISSN 1631-073X, 04/2015, Volume 353, Issue 4, pp. 357 - 362
We introduce the notions of Atiyah class and Todd class of a differential graded vector bundle with respect to a differential graded Lie algebroid... 
MATHEMATICS | DRINFELD DOUBLES | ALGEBROIDS | LIE BIALGEBROIDS | EHRESMANN DOUBLES | Algebra | Mathematics - Differential Geometry
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
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
Advances in Mathematics, ISSN 0001-8708, 2010, Volume 223, Issue 4, pp. 1236 - 1275
A VB -algebroid is essentially defined as a Lie algebroid object in the category of vector bundles... 
Characteristic classes | Representation | Superconnection | Double category | Lie algebroid | MATHEMATICS | COHOMOLOGY
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
Letters in Mathematical Physics, ISSN 0377-9017, 11/2009, Volume 90, Issue 1, pp. 175 - 200
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 4/2016, Volume 181, Issue 1, pp. 137 - 175
... $$p+q$$ p + q vector bundle V on a smooth complex variety X equipped with a flag of subbundles and a splitting of V as a direct sum of subbundles of ranks p and q... 
Geometry | 14M27 | Equivariant cohomology | Degeneracy loci | Flag variety | Mathematics | Symmetric subgroup | MATHEMATICS | DETERMINANTAL FORMULAS | CLASSICAL-GROUPS | DOUBLE SCHUBERT POLYNOMIALS | VARIETIES | SUBGROUPS | Algebraic Geometry | Combinatorics | Algebraic Topology | Representation Theory
Journal Article
Turkish Journal of Mathematics, ISSN 1300-0098, 2017, Volume 41, Issue 4, pp. 854 - 868
In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle... 
Double vector bundle | Canonical involution | Tangent bundle of higher order | Second order jets | Double jet bundle | MATHEMATICS | second order jets | double vector bundle | canonical involution | tangent bundle of higher order
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 2010, Volume 60, Issue 4, pp. 581 - 598
...) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles... 
Double vector bundle | Duality | Affine bundle | Vector bundle | Affine space | MATHEMATICS, APPLIED | AV-DIFFERENTIAL GEOMETRY | PHYSICS, MATHEMATICAL
Journal Article
Advances in Mathematics, ISSN 0001-8708, 04/2017, Volume 311, pp. 469 - 480
Given a closed manifold M and a vector bundle ξ of rank n over M, by gluing two copies of the disc bundle of ξ... 
Ricci curvature | Isoparametric foliation | Sphere bundle | Vector bundle | Double manifold | MATHEMATICS | PRINCIPAL CURVATURES | HYPERSURFACES | CLASSIFICATION
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 09/2019, Volume 292, Issue 9, pp. 2092 - 2100
...−VB of double vector bundles in terms of the AF‐bilinear maps ⋄F:UF×VF→WF, where AF are Weil algebras and UF,VF,WF are finite dimensional (over R) AF‐modules... 
natural operator | (product preserving) gauge bundle functor | 58A05 | (double) vector bundle | 58A32 | Weil algebra | 58A20 | MATHEMATICS | Algebra
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2019, Volume 372, Issue 3, pp. 1783 - 1816
.... We show that any aCM vector bundle of rank two on the double plane is a direct sum of line bundles... 
double plane | VARIETY | MATHEMATICS | REPRESENTATION TYPE | MODULES | RANK-2 | SPACES | COHEN-MACAULAY BUNDLES | Arithmetically Cohen-Macaulay sheaf | layered sheaf | VECTOR-BUNDLES
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
Journal of Algebra, ISSN 0021-8693, 01/2017, Volume 469, pp. 251 - 266
We study the projective normality of a minimal surface X which is a ramified double covering over a rational surface S with dim⁡|−KS|≥1. In particular Horikawa... 
Projective normality | Adjoint divisor | Double covering | MATHEMATICS | K-3 SURFACES | ALGEBRAIC-SURFACES | VARIETIES | GENERAL TYPE | KOSZUL COHOMOLOGY | VECTOR-BUNDLES
Journal Article
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