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dc.contributor.authorGrady, Ryan
dc.contributor.authorGwilliam, Owen
dc.date.accessioned2021-03-08T18:42:59Z
dc.date.available2021-03-08T18:42:59Z
dc.date.issued2018-02
dc.identifier.citationGrady, Ryan, and Owen Gwilliam. “Lie Algebroids As L [infinity] Spaces.” Journal of the Institute of Mathematics of Jussieu 19, no. 2 (February 13, 2018): 487–535. doi:10.1017/s1474748018000075.en_US
dc.identifier.issn1474-7480
dc.identifier.urihttps://scholarworks.montana.edu/xmlui/handle/1/16144
dc.description.abstractIn this paper, we relate Lie algebroids to Costello’s version of derived geometry. For instance, we show that each Lie algebroid – and the natural generalization to dg Lie algebroids – provides an (essentially unique) L infinity space. More precisely, we construct a faithful functor from the category of Lie algebroids to the category of L infinity spaces. Then we show that for each Lie algebroid L, there is a fully faithful functor from the category of representations up to homotopy of L to the category of vector bundles over the associated L infinity space. Indeed, this functor sends the adjoint complex of L to the tangent bundle of the L infinity space. Finally, we show that a shifted symplectic structure on a dg Lie algebroid produces a shifted symplectic structure on the associated L infinity space.en_US
dc.language.isoen_USen_US
dc.titleLie Algebroids As L[infinity] Spacesen_US
dc.typeArticleen_US
mus.citation.extentfirstpage487en_US
mus.citation.extentlastpage535en_US
mus.citation.issue2en_US
mus.citation.journaltitleJournal of the Institute of Mathematics of Jussieuen_US
mus.citation.volume19en_US
mus.identifier.doi10.1017/s1474748018000075en_US
mus.relation.collegeCollege of Letters & Scienceen_US
mus.relation.departmentMathematical Sciences.en_US
mus.relation.universityMontana State University - Bozemanen_US
mus.data.thumbpage4en_US


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