{"title":"拉格朗日NQ子曼形体的变形","authors":"Miquel Cueca , Jonas Schnitzer","doi":"10.1016/j.aim.2024.109952","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper we prove graded versions of the Darboux Theorem and Weinstein's Lagrangian tubular neighbourhood Theorem in order to study the deformation theory of Lagrangian <em>NQ</em>-submanifolds of degree <em>n</em> symplectic <em>NQ</em>-manifolds. Using Weinstein's Lagrangian tubular neighbourhood Theorem, we attach to every Lagrangian <em>NQ</em>-submanifold an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebra, which controls its deformation theory. The main examples are coisotropic submanifolds of Poisson manifolds and (higher) Dirac structures with support in (higher) Courant algebroids.</div></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0001870824004675/pdfft?md5=5940eacdc2d09ddd157ad0d959322302&pid=1-s2.0-S0001870824004675-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Deformations of Lagrangian NQ-submanifolds\",\"authors\":\"Miquel Cueca , Jonas Schnitzer\",\"doi\":\"10.1016/j.aim.2024.109952\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper we prove graded versions of the Darboux Theorem and Weinstein's Lagrangian tubular neighbourhood Theorem in order to study the deformation theory of Lagrangian <em>NQ</em>-submanifolds of degree <em>n</em> symplectic <em>NQ</em>-manifolds. Using Weinstein's Lagrangian tubular neighbourhood Theorem, we attach to every Lagrangian <em>NQ</em>-submanifold an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebra, which controls its deformation theory. The main examples are coisotropic submanifolds of Poisson manifolds and (higher) Dirac structures with support in (higher) Courant algebroids.</div></div>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-09-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0001870824004675/pdfft?md5=5940eacdc2d09ddd157ad0d959322302&pid=1-s2.0-S0001870824004675-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0001870824004675\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870824004675","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
在本文中，我们证明了达布定理和温斯坦拉格朗日管状邻域定理的分级版本，以研究 n 度交映 NQ-manifolds的拉格朗日 NQ-submanifolds的变形理论。利用韦恩斯坦拉格朗日管状邻域定理，我们给每个拉格朗日 NQ 子曼形体附加了一个 L∞ 代数，这个代数控制着它的变形理论。主要的例子是泊松流形的各向同性子流形，以及在（高）库朗特实体中具有支持的（高）狄拉克结构。
In this paper we prove graded versions of the Darboux Theorem and Weinstein's Lagrangian tubular neighbourhood Theorem in order to study the deformation theory of Lagrangian NQ-submanifolds of degree n symplectic NQ-manifolds. Using Weinstein's Lagrangian tubular neighbourhood Theorem, we attach to every Lagrangian NQ-submanifold an -algebra, which controls its deformation theory. The main examples are coisotropic submanifolds of Poisson manifolds and (higher) Dirac structures with support in (higher) Courant algebroids.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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