{"title":"泊松几何中的同伦BV代数","authors":"Christopher Braun, A. Lazarev","doi":"10.1090/S0077-1554-2014-00216-8","DOIUrl":null,"url":null,"abstract":"We define and study the degeneration property for $ \\mathrm {BV}_\\infty $ algebras and show that it implies that the underlying $ L_{\\infty }$ algebras are homotopy abelian. The proof is based on a generalisation of the well-known identity $ \\Delta (e^{\\xi })=e^{\\xi }\\Big (\\Delta (\\xi )+\\frac {1}{2}[\\xi ,\\xi ]\\Big )$ which holds in all BV algebras. As an application we show that the higher Koszul brackets on the cohomology of a manifold supplied with a generalised Poisson structure all vanish. - See more at: http://www.ams.org/journals/mosc/2013-74-00/S0077-1554-2014-00216-8/#sthash.pBIIcZKa.dpuf","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"74 1","pages":"217-227"},"PeriodicalIF":0.0000,"publicationDate":"2013-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00216-8","citationCount":"27","resultStr":"{\"title\":\"Homotopy BV algebras in Poisson geometry\",\"authors\":\"Christopher Braun, A. Lazarev\",\"doi\":\"10.1090/S0077-1554-2014-00216-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We define and study the degeneration property for $ \\\\mathrm {BV}_\\\\infty $ algebras and show that it implies that the underlying $ L_{\\\\infty }$ algebras are homotopy abelian. The proof is based on a generalisation of the well-known identity $ \\\\Delta (e^{\\\\xi })=e^{\\\\xi }\\\\Big (\\\\Delta (\\\\xi )+\\\\frac {1}{2}[\\\\xi ,\\\\xi ]\\\\Big )$ which holds in all BV algebras. As an application we show that the higher Koszul brackets on the cohomology of a manifold supplied with a generalised Poisson structure all vanish. - See more at: http://www.ams.org/journals/mosc/2013-74-00/S0077-1554-2014-00216-8/#sthash.pBIIcZKa.dpuf\",\"PeriodicalId\":37924,\"journal\":{\"name\":\"Transactions of the Moscow Mathematical Society\",\"volume\":\"74 1\",\"pages\":\"217-227\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-04-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00216-8\",\"citationCount\":\"27\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the Moscow Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/S0077-1554-2014-00216-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the Moscow Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/S0077-1554-2014-00216-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
We define and study the degeneration property for $ \mathrm {BV}_\infty $ algebras and show that it implies that the underlying $ L_{\infty }$ algebras are homotopy abelian. The proof is based on a generalisation of the well-known identity $ \Delta (e^{\xi })=e^{\xi }\Big (\Delta (\xi )+\frac {1}{2}[\xi ,\xi ]\Big )$ which holds in all BV algebras. As an application we show that the higher Koszul brackets on the cohomology of a manifold supplied with a generalised Poisson structure all vanish. - See more at: http://www.ams.org/journals/mosc/2013-74-00/S0077-1554-2014-00216-8/#sthash.pBIIcZKa.dpuf
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