Journal of Geometry and Physics, ISSN 0393-0440, 08/2019, Volume 142, pp. 254 - 273

Pre-Courant algebroids are ‘Courant algebroids’ without the Jacobi identity for the Courant–Dorfman bracket. We examine the corresponding supermanifold...

Q-manifolds | Supermanifolds | Courant algebroids | VB-Courant algebroids | Cochain complex | TANGENT LIFTS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DIRAC STRUCTURES | GRADED BUNDLES | MANIFOLDS | GEOMETRY

Q-manifolds | Supermanifolds | Courant algebroids | VB-Courant algebroids | Cochain complex | TANGENT LIFTS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DIRAC STRUCTURES | GRADED BUNDLES | MANIFOLDS | GEOMETRY

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 10/2016, Volume 289, Issue 14-15, pp. 1893 - 1908

In this paper, we introduce the notion of a left‐symmetric algebroid, which is a generalization of a left‐symmetric algebra from a vector space to a vector...

Left‐symmetric algebroids | symplectic Lie algeboids | cohomologies | 18B40 | deformations | 17B65 | Left-symmetric algebroids | MATHEMATICS | YANG-BAXTER EQUATION | ABELIAN PHASE SPACES | LIE ALGEBROIDS | ALGEBRAIC APPROACH

Left‐symmetric algebroids | symplectic Lie algeboids | cohomologies | 18B40 | deformations | 17B65 | Left-symmetric algebroids | MATHEMATICS | YANG-BAXTER EQUATION | ABELIAN PHASE SPACES | LIE ALGEBROIDS | ALGEBRAIC APPROACH

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2019, Volume 354, p. 106750

This paper studies the role of dg-Lie algebroids in derived deformation theory. More precisely, we provide an equivalence between the homotopy theories of...

Formal moduli problem | Koszul duality | Lie algebroid | koszul duality | formal moduli problem | MATHEMATICS | COMPLEX | MODULES | DEFORMATIONS

Formal moduli problem | Koszul duality | Lie algebroid | koszul duality | formal moduli problem | MATHEMATICS | COMPLEX | MODULES | DEFORMATIONS

Journal Article

JOURNAL OF MATHEMATICAL PHYSICS, ISSN 0022-2488, 09/2015, Volume 56, Issue 9, p. 92302

Courant algebroids, originally used to study integrability conditions for Dirac structures, have turned out to be of central importance to study the effective...

BRACKETS | SUPERSPACE | DUALITY | LIE BIALGEBROIDS | QUANTIZATION | PHYSICS, MATHEMATICAL | DEFORMATION-THEORY | String theory | Field theory | Deformation | Integral calculus | Brackets | Supergravity | CORRECTIONS | SIGMA MODEL | MATHEMATICAL SOLUTIONS | SUPERGRAVITY | STRING MODELS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | STRING THEORY

BRACKETS | SUPERSPACE | DUALITY | LIE BIALGEBROIDS | QUANTIZATION | PHYSICS, MATHEMATICAL | DEFORMATION-THEORY | String theory | Field theory | Deformation | Integral calculus | Brackets | Supergravity | CORRECTIONS | SIGMA MODEL | MATHEMATICAL SOLUTIONS | SUPERGRAVITY | STRING MODELS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | STRING THEORY

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 08/2018, Volume 116, pp. 1 - 39

We define Dorfman connections, which are to Courant algebroids what connections are to Lie algebroids. We illustrate this analogy with examples. In particular,...

Linear connections | VB-algebroids | Courant algebroids | Lie bialgebroids | Linear splittings | IM-2-forms | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | INTEGRATION | DIRAC STRUCTURES | LIE ALGEBROIDS

Linear connections | VB-algebroids | Courant algebroids | Lie bialgebroids | Linear splittings | IM-2-forms | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATIONS | INTEGRATION | DIRAC STRUCTURES | LIE ALGEBROIDS

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 11/2017, Volume 121, pp. 15 - 32

In this paper, first we modify the definition of a Hom-Lie algebroid introduced by Laurent-Gengoux and Teles and give its equivalent dual description. Many...

Hom-Poisson manifold | Hom-Lie algebra | Hom-Courant algebroid | Hom-Lie algebroid | Hom-Lie bialgebroid | Algebra

Hom-Poisson manifold | Hom-Lie algebra | Hom-Courant algebroid | Hom-Lie algebroid | Hom-Lie bialgebroid | Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 07/2018, Volume 505, pp. 456 - 481

We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme X, and a coherent sheaf of...

Lie algebroid extensions | Lie algebroid cohomology | Free Lie algebroids | MATHEMATICS | Mathematical Physics | Mathematics

Lie algebroid extensions | Lie algebroid cohomology | Free Lie algebroids | MATHEMATICS | Mathematical Physics | Mathematics

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 10/2011, Volume 44, Issue 42, pp. 425206 - 35

We show how to reduce, under certain regularity conditions, a Poisson-Nijenhuis Lie algebroid to a symplectic-Nijenhuis Lie algebroid with a nondegenerate...

PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | TANGENT | Manifolds | Reduction | Tensors | Mathematical analysis | Regularity | Lie groups

PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | TANGENT | Manifolds | Reduction | Tensors | Mathematical analysis | Regularity | Lie groups

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 9/2018, Volume 108, Issue 9, pp. 2099 - 2137

We define the transgression functor which associates with a (higher-dimensional) Courant algebroid on a manifold a Lie algebroid on the shifted tangent bundle...

Geometry | Courant algebroid | Theoretical, Mathematical and Computational Physics | Complex Systems | Lie algebroid | Differential graded manifold | 53D15 | Group Theory and Generalizations | 58A50 | Physics | HIGHER ANALOGS | MANIFOLDS | PHYSICS, MATHEMATICAL

Geometry | Courant algebroid | Theoretical, Mathematical and Computational Physics | Complex Systems | Lie algebroid | Differential graded manifold | 53D15 | Group Theory and Generalizations | 58A50 | Physics | HIGHER ANALOGS | MANIFOLDS | PHYSICS, MATHEMATICAL

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 06/2017, Volume 116, pp. 187 - 203

We give a notion of hom-left-symmetric algebroids, which are a generalization of hom-left symmetric algebras. We construct several examples of hom-Lie...

Representation | Cohomology | Hom-left-symmetric algebroid | Hom-Lie algebroid | MATHEMATICS | DEFORMATIONS | PHYSICS, MATHEMATICAL | Algebra

Representation | Cohomology | Hom-left-symmetric algebroid | Hom-Lie algebroid | MATHEMATICS | DEFORMATIONS | PHYSICS, MATHEMATICAL | Algebra

Journal Article

Applied Categorical Structures, ISSN 0927-2852, 10/2019, Volume 27, Issue 5, pp. 493 - 534

We construct Quillen equivalent semi-model structures on the categories of dg-Lie algebroids and L∞-algebroids over a commutative dg-algebra in characteristic...

Computer Science(all) | Lie algebroid cohomology | Model category | Theoretical Computer Science | Dg-Lie algebroid | Geometry | 55U35 | Convex and Discrete Geometry | Mathematics | Theory of Computation | 18G55 | 55U15 | Mathematical Logic and Foundations | MATHEMATICS | CATEGORY | Analysis | Algebra

Computer Science(all) | Lie algebroid cohomology | Model category | Theoretical Computer Science | Dg-Lie algebroid | Geometry | 55U35 | Convex and Discrete Geometry | Mathematics | Theory of Computation | 18G55 | 55U15 | Mathematical Logic and Foundations | MATHEMATICS | CATEGORY | Analysis | Algebra

Journal Article

Canadian Mathematical Bulletin, ISSN 0008-4395, 09/2018, Volume 61, Issue 3, pp. 588 - 607

In this paper, we first discuss the relation between VB-Courant algebroids and E-Courant algebroids, and we construct some examples of E-Courant algebroids....

Algebroid-nijenhuis structure | VB-Courant algebroid | E-Courant algebroid | Omni-Lie algebroid | Generalized complex structure | algebroid-Nijenhuis structure | MATHEMATICS | generalized complex structure | REDUCTION | LIE BIALGEBROIDS | MANIFOLDS | COMPLEX STRUCTURES | omni-Lie algebroid

Algebroid-nijenhuis structure | VB-Courant algebroid | E-Courant algebroid | Omni-Lie algebroid | Generalized complex structure | algebroid-Nijenhuis structure | MATHEMATICS | generalized complex structure | REDUCTION | LIE BIALGEBROIDS | MANIFOLDS | COMPLEX STRUCTURES | omni-Lie algebroid

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 06/2017, Volume 19, Issue 3, p. 1650034

We study the extension of a Lie algebroid by a representation up to homotopy, including semidirect products of a Lie algebroid with such representations. The...

Representation up to homotopy | integration | Lie 2-groupoids | Courant algebroids | Lie 2-algebroids | BRACKETS | MATHEMATICS, APPLIED | REPRESENTATIONS | HOMOTOPY | L-INFINITY-ALGEBRAS | MATHEMATICS | GROUPOIDS | GEOMETRY

Representation up to homotopy | integration | Lie 2-groupoids | Courant algebroids | Lie 2-algebroids | BRACKETS | MATHEMATICS, APPLIED | REPRESENTATIONS | HOMOTOPY | L-INFINITY-ALGEBRAS | MATHEMATICS | GROUPOIDS | GEOMETRY

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 6/2017, Volume 2017, Issue 6, pp. 1 - 14

We explicitly show how the field dependent 2-cocycle that arises in the current algebra of 4 dimensional asymptotically flat spacetimes can be used as a...

Anomalies in Field and String Theories | Classical Theories of Gravity | Gauge-gravity correspondence | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | GENERAL-RELATIVITY | GREEN-FUNCTIONS | ASYMPTOTIC SYMMETRIES | HARMONIC SUPERGRAPHS | GRAVITATIONAL WAVES | BLACK-HOLE | GRAVITY | PHYSICS, PARTICLES & FIELDS | Algebra | Shear | Current algebra | Asymptotic properties | News | Lie groups | Mapping | Celestial sphere | Cylinders | General Relativity and Quantum Cosmology | Nuclear and particle physics. Atomic energy. Radioactivity | Physique | High Energy Physics - Theory

Anomalies in Field and String Theories | Classical Theories of Gravity | Gauge-gravity correspondence | Quantum Physics | Conformal and W Symmetry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | GENERAL-RELATIVITY | GREEN-FUNCTIONS | ASYMPTOTIC SYMMETRIES | HARMONIC SUPERGRAPHS | GRAVITATIONAL WAVES | BLACK-HOLE | GRAVITY | PHYSICS, PARTICLES & FIELDS | Algebra | Shear | Current algebra | Asymptotic properties | News | Lie groups | Mapping | Celestial sphere | Cylinders | General Relativity and Quantum Cosmology | Nuclear and particle physics. Atomic energy. Radioactivity | Physique | High Energy Physics - Theory

Journal Article

Canadian Journal of Physics, ISSN 0008-4204, 2019, Volume 97, Issue 2, pp. 145 - 154

The approach to nonholonomic Ricci flows and geometric evolution of regular Lagrange systems (S. Vacaru. J. Math. Phys. 49 , 043504 (2008); Ibid. Rep. Math....

Ricci flows | Lie algebroids | algébroïdes de Lie | Lagrange mechanics | analogous gravity | gravité | flot de Ricci | équations dynamiques | Analogous gravity | MECHANICS | PHYSICS, MULTIDISCIPLINARY | EINSTEIN | FINSLER | GRAVITY | Thermodynamics | Usage | Models | Lie algebras | Mechanics (physics) | Gravitation | Arches | Mechanics | Evolution | Mathematical models | Gradient flow | Prolongation

Ricci flows | Lie algebroids | algébroïdes de Lie | Lagrange mechanics | analogous gravity | gravité | flot de Ricci | équations dynamiques | Analogous gravity | MECHANICS | PHYSICS, MULTIDISCIPLINARY | EINSTEIN | FINSLER | GRAVITY | Thermodynamics | Usage | Models | Lie algebras | Mechanics (physics) | Gravitation | Arches | Mechanics | Evolution | Mathematical models | Gradient flow | Prolongation

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 06/2013, Volume 68, pp. 69 - 75

We define hom-Lie algebroids, a definition that may seem cumbersome at first, but which is justified, first, by a one-to-one correspondence with...

Hom-structures | Gerstenhaber algebra | Lie algebroids | Hom-Poisson structures | MATHEMATICS, APPLIED | DEFORMATIONS | PHYSICS, MATHEMATICAL | Mathematics

Hom-structures | Gerstenhaber algebra | Lie algebroids | Hom-Poisson structures | MATHEMATICS, APPLIED | DEFORMATIONS | PHYSICS, MATHEMATICAL | Mathematics

Journal Article

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. Through a suitable reformulation of their...

Poisson groupoids | VB-algebroids | Double Lie algebroids | VB-groupoids | LA-groupoids | BRACKETS | INTEGRABILITY | REPRESENTATIONS | 2ND-ORDER GEOMETRY | HOMOTOPY | BIALGEBROIDS | MATHEMATICS | INTEGRATION | DUALITY

Poisson groupoids | VB-algebroids | Double Lie algebroids | VB-groupoids | LA-groupoids | BRACKETS | INTEGRABILITY | REPRESENTATIONS | 2ND-ORDER GEOMETRY | HOMOTOPY | BIALGEBROIDS | MATHEMATICS | INTEGRATION | DUALITY

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 02/2020, Volume 148, p. 103541

This work extends both classical results on Atiyah Lie algebroids and previous developments carried out by some of the authors on Ehresmann connections on...

Cartan connection | Diffeomorphisms | Lie algebroid | Gravity | Anomalies | Gauge transformations | MATHEMATICS | PHYSICS, MATHEMATICAL | Mathematical Physics | Physics

Cartan connection | Diffeomorphisms | Lie algebroid | Gravity | Anomalies | Gauge transformations | MATHEMATICS | PHYSICS, MATHEMATICAL | Mathematical Physics | Physics

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 3/2018, Volume 108, Issue 3, pp. 737 - 756

Cartan–Lie algebroids, i.e., Lie algebroids equipped with a compatible connection, permit the definition of an adjoint representation, on the fiber as well as...

Cartan connections | 53B21 | Lie algebroids | Lie groupoids | 53C12 | Theoretical, Mathematical and Computational Physics | Complex Systems | Multiplicative distributions | 53B05 | Riemannian submersions | Physics | 58H05 | Geometry | Jet spaces and jet bundles | 58A20 | Group Theory and Generalizations | 58A30 | SYMMETRIES | PHYSICS, MATHEMATICAL | Mathematics - Differential Geometry | Mathematics | Differential Geometry | Mathematical Physics

Cartan connections | 53B21 | Lie algebroids | Lie groupoids | 53C12 | Theoretical, Mathematical and Computational Physics | Complex Systems | Multiplicative distributions | 53B05 | Riemannian submersions | Physics | 58H05 | Geometry | Jet spaces and jet bundles | 58A20 | Group Theory and Generalizations | 58A30 | SYMMETRIES | PHYSICS, MATHEMATICAL | Mathematics - Differential Geometry | Mathematics | Differential Geometry | Mathematical Physics

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 11/2018, Volume 133, pp. 287 - 302

We define the notion of hom-Batalin–Vilkovisky algebras and strong differential hom-Gerstenhaber algebras as a special class of hom-Gerstenhaber algebras and...

Hom-Gerstenhaber algebras | Hom-Lie–Rinehart algebras | Hom-Poisson structures | Hom-Lie algebroids | MATHEMATICS | COHOMOLOGY | DEFORMATIONS | PHYSICS, MATHEMATICAL | Hom-Lie-Rinehart algebras | Algebra

Hom-Gerstenhaber algebras | Hom-Lie–Rinehart algebras | Hom-Poisson structures | Hom-Lie algebroids | MATHEMATICS | COHOMOLOGY | DEFORMATIONS | PHYSICS, MATHEMATICAL | Hom-Lie-Rinehart algebras | Algebra

Journal Article

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