Hamilton Lie algebroids over Dirac structures and sigma models

Noriaki Ikeda

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arXiv · 2309.10996

Hamilton Lie algebroids over Dirac structures and sigma models

Noriaki Ikeda

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Abstract

We propose a Hamiltonian Lie algebroid and a momentum section over a Dirac structure as a generalization of a Hamiltonian Lie algebroid over a pre-symplectic manifold and one over a Poisson manifold. A Hamiltonian Lie algebroid and a momentum section are generalizations of a Hamiltonian G-space and a momentum map over a symplectic manifold. We show some properties of a new Hamiltonian Lie algebroid, and construct the mechanics with this structure as an application, which are sigma models called the gauged Poisson sigma model and the gauged Dirac sigma model.

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Noriaki Ikeda. 2026-04-26. Hamilton Lie algebroids over Dirac structures and sigma models. https://arxiv.org/abs/2309.10996

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