{"title":"分次向量场的动态对称性","authors":"E. Azizpour, Dordi Mohammad Atayi","doi":"10.1080/1726037X.2019.1668146","DOIUrl":null,"url":null,"abstract":"Abstract Suppose that = (M, M ) is a graded manifold and consider a direct subsheaf of DerM and a graded vector field Γ on ; both satisfying certain conditions. We associate to the graded vector field Γ ∈ DerM, a set of 1-forms and show that if φ ∈ is a non-degenerate graded 1-form and X ∈ DerM such that for some superfunction f on , then the superfunction F = f − J(φ)(X) satisfies . This result, generalizes the conditions under which there exist a solution for the inverse problem.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"17 1","pages":"187 - 203"},"PeriodicalIF":0.4000,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2019.1668146","citationCount":"0","resultStr":"{\"title\":\"Dynamical Symmetries for Graded Vector Fields\",\"authors\":\"E. Azizpour, Dordi Mohammad Atayi\",\"doi\":\"10.1080/1726037X.2019.1668146\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Suppose that = (M, M ) is a graded manifold and consider a direct subsheaf of DerM and a graded vector field Γ on ; both satisfying certain conditions. We associate to the graded vector field Γ ∈ DerM, a set of 1-forms and show that if φ ∈ is a non-degenerate graded 1-form and X ∈ DerM such that for some superfunction f on , then the superfunction F = f − J(φ)(X) satisfies . This result, generalizes the conditions under which there exist a solution for the inverse problem.\",\"PeriodicalId\":42788,\"journal\":{\"name\":\"Journal of Dynamical Systems and Geometric Theories\",\"volume\":\"17 1\",\"pages\":\"187 - 203\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2019-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/1726037X.2019.1668146\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamical Systems and Geometric Theories\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/1726037X.2019.1668146\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamical Systems and Geometric Theories","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/1726037X.2019.1668146","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Abstract Suppose that = (M, M ) is a graded manifold and consider a direct subsheaf of DerM and a graded vector field Γ on ; both satisfying certain conditions. We associate to the graded vector field Γ ∈ DerM, a set of 1-forms and show that if φ ∈ is a non-degenerate graded 1-form and X ∈ DerM such that for some superfunction f on , then the superfunction F = f − J(φ)(X) satisfies . This result, generalizes the conditions under which there exist a solution for the inverse problem.
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