Higher nonabelian omni-Lie algebroids

Banach Lie Algebroids

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/v10157-011-0035-y ◽

2011 ◽

Vol 57 (2) ◽

pp. 409-416

Author(s):

Mihai Anastasiei

Keyword(s):

Differential Equations ◽

Smooth Manifold ◽

Vector Bundles ◽

Second Order ◽

Lie Algebroids ◽

Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

Download Full-text

Complex Lie algebroids and Finsler manifold in time-dependent fractal dimension and their associated decomplexifications

Differential Geometry and its Applications ◽

10.1016/j.difgeo.2021.101775 ◽

2021 ◽

Vol 77 ◽

pp. 101775

Author(s):

Rami Ahmad El-Nabulsi

Keyword(s):

Fractal Dimension ◽

Finsler Manifold ◽

Lie Algebroids ◽

Time Dependent

Download Full-text

Drinfel’d doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids

Electronic Research Announcements of the American Mathematical Society ◽

10.1090/s1079-6762-98-00050-x ◽

1998 ◽

Vol 4 (11) ◽

pp. 74-87 ◽

Cited By ~ 15

Author(s):

K. C. H. Mackenzie

Keyword(s):

Lie Algebroids ◽

Drinfel'd Doubles

Download Full-text

Tulczyjew triples and higher poisson/schouten structures on lie algebroids

Reports on Mathematical Physics ◽

10.1016/s0034-4877(10)80030-8 ◽

2010 ◽

Vol 66 (2) ◽

pp. 251-276 ◽

Cited By ~ 3

Author(s):

Andrew James Bruce

Keyword(s):

Lie Algebroids

Download Full-text

Formulation of gauge theories on transitive Lie algebroids

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2012.11.005 ◽

2013 ◽

Vol 64 ◽

pp. 174-191 ◽

Cited By ~ 6

Author(s):

Cédric Fournel ◽

Serge Lazzarini ◽

Thierry Masson

Keyword(s):

Gauge Theories ◽

Lie Algebroids

Download Full-text

A SURVEY OF LAGRANGIAN MECHANICS AND CONTROL ON LIE ALGEBROIDS AND GROUPOIDS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887806001211 ◽

2006 ◽

Vol 03 (03) ◽

pp. 509-558 ◽

Cited By ~ 26

Author(s):

JORGE CORTÉS ◽

MANUEL DE LEÓN ◽

JUAN C. MARRERO ◽

D. MARTÍN DE DIEGO ◽

EDUARDO MARTÍNEZ

Keyword(s):

Control Systems ◽

Classical Field Theory ◽

Nonholonomic Constraints ◽

Classical Field ◽

Lie Algebroids ◽

Hamiltonian Mechanics ◽

Lagrangian Mechanics ◽

Geometric Description ◽

Lagrangian And Hamiltonian Mechanics ◽

And Control

In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical control systems, Discrete Mechanics and extensions to Classical Field Theory within a single framework. Various examples along the discussion illustrate the soundness of the approach.

Download Full-text