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arXiv · 0905.4585

K-symplectic formalism on Lie algebroids

M. de Leon·D. Martin de Diego·M. Salgado·S. Vilariño
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Abstract

In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of k-symplectic geometry. We discuss the relation between Lagrangian and Hamiltonian descriptions through a convenient notion of Legendre transformation. The theory is a natural generalization of the standard one; in addition, other interesting examples are studied, in particular, systems with symmetry and Poisson sigma models.

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M. de Leon, D. Martin de Diego, M. Salgado, S. Vilariño. 2009-05-28. K-symplectic formalism on Lie algebroids. https://doi.org/10.1088/1751-8113%2F42%2F38%2F385209

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