[2309.10996] Hamilton Lie algebroids over Dirac structures and sigma models Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Differential Geometry arXiv:2309.10996 (math) [Submitted on 20 Sep 2023 ( v1 ), last revised 26 Apr 2026 (this version, v2)] Title: Hamilton Lie algebroids over Dirac structures and sigma models Authors: Noriaki Ikeda View a PDF of the paper titled Hamilton Lie algebroids over Dirac structures and sigma models, by Noriaki Ikeda View PDF HTML (experimental) 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. Comments: 37pages Subjects: Differential Geometry (math.DG) ; High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Symplectic Geometry (math.SG) Cite as: arXiv:2309.10996 [math.DG] (or arXiv:2309.10996v2 [math.DG] for this version) https://doi.org/10.48550/arXiv.2309.10996 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Noriaki Ikeda [ view email ] [v1] Wed, 20 Sep 2023 01:30:55 UTC (29 KB) [v2] Sun, 26 Apr 2026 01:11:58 UTC (32 KB) Full-text links: Access Paper: View a PDF of the paper titled Hamilton Lie algebroids over Dirac structures and sigma models, by Noriaki Ikeda View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2023-09 Change to browse by: hep-th math math-ph math.MP math.SG References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from