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arXiv · 2106.14355

$\omega$-Symplectic algebra and Hamiltonian vector fields

Patrícia Hernandes Baptistelli·Maria Elenice Rodrigues Hernandes·Eralcilene Moreira Terezio
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Abstract

The purpose of this paper is presenting a theoretical basis for the study of $\omega$-Hamiltonian vector fields in a more general approach than the classical one. We introduce the concepts of $\omega$-symplectic group and $\omega$-semisymplectic group, and describe some of their properties. We show that the Lie algebra of such groups is a useful tool in the recognition of an $\omega$-Hamiltonian vector field defined on a symplectic vector space $(V,\omega)$ with respect to coordinates that are not necessarily symplectic.

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Patrícia Hernandes Baptistelli, Maria Elenice Rodrigues Hernandes, Eralcilene Moreira Terezio. 2021-06-28. $\omega$-Symplectic algebra and Hamiltonian vector fields. https://arxiv.org/abs/2106.14355

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