{"title":"狄拉克结构和模型上的汉密尔顿李代数","authors":"Noriaki Ikeda","doi":"10.1016/j.difgeo.2025.102277","DOIUrl":null,"url":null,"abstract":"<div><div>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 generalize a Hamiltonian <em>G</em>-space and a momentum map over a symplectic manifold. We prove some properties of this new Hamiltonian Lie algebroid and construct a mechanics based on this structure as an application. These new mechanics are called the gauged Poisson sigma model and the gauged Dirac sigma model.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102277"},"PeriodicalIF":0.7000,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hamilton Lie algebroids over Dirac structures and sigma models\",\"authors\":\"Noriaki Ikeda\",\"doi\":\"10.1016/j.difgeo.2025.102277\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>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 generalize a Hamiltonian <em>G</em>-space and a momentum map over a symplectic manifold. We prove some properties of this new Hamiltonian Lie algebroid and construct a mechanics based on this structure as an application. These new mechanics are called the gauged Poisson sigma model and the gauged Dirac sigma model.</div></div>\",\"PeriodicalId\":51010,\"journal\":{\"name\":\"Differential Geometry and its Applications\",\"volume\":\"100 \",\"pages\":\"Article 102277\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-08-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Geometry and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S092622452500052X\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S092622452500052X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Hamilton Lie algebroids over Dirac structures and sigma models
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 generalize a Hamiltonian G-space and a momentum map over a symplectic manifold. We prove some properties of this new Hamiltonian Lie algebroid and construct a mechanics based on this structure as an application. These new mechanics are called the gauged Poisson sigma model and the gauged Dirac sigma model.
期刊介绍:
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.