scholarly journals The Weil algebra and the secondary characteristic homomorphism of regular Lie algebroids

2001 ◽  
Vol 54 ◽  
pp. 135-173 ◽  
Author(s):  
Jan Kubarski
Keyword(s):  
Lie Algebroids ◽  
Weil Algebra ◽  
Secondary Characteristic

Chern–Simons forms for ℝ-linear connections on Lie algebroids

2018 ◽  
Vol 29 (13) ◽  
pp. 1850094
Author(s):  
Bogdan Balcerzak
Keyword(s):  
Chern Character ◽  
Lie Algebroids ◽  
Characteristic Classes ◽  
Linear Connections ◽  
Secondary Characteristic Classes ◽  
Chern Simons ◽  
Secondary Characteristic

This paper considers the Chern–Simons forms for [Formula: see text]-linear connections on Lie algebroids. A generalized Chern–Simons formula for such [Formula: see text]-linear connections is obtained. We apply it to define the Chern character and secondary characteristic classes for [Formula: see text]-linear connections of Lie algebroids.

Banach Lie Algebroids

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.

Higher nonabelian omni-Lie algebroids

2021 ◽  
pp. 104277
Author(s):  
Bi Yanhui ◽  
Fan Hongtao
Keyword(s):  
Lie Algebroids

scholarly journals Formulation of gauge theories on transitive Lie algebroids

2013 ◽  
Vol 64 ◽  
pp. 174-191 ◽  
Author(s):  
Cédric Fournel ◽  
Serge Lazzarini ◽  
Thierry Masson
Keyword(s):  
Gauge Theories ◽  
Lie Algebroids

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

2006 ◽  
Vol 03 (03) ◽  
pp. 509-558 ◽  
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.

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