BFV-complex and higher homotopy structures

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dc.creatorSchaetz, Florian
dc.date2006-11-29
dc.date2008-10-14
dc.date.accessioned2026-07-07T10:09:41Z
dc.date.available2026-07-07T10:09:41Z
dc.descriptionWe present a connection between the BFV-complex (abbreviation for Batalin-Fradkin-Vilkovisky complex) and the so-called strong homotopy Lie algebroid associated to a coisotropic submanifold of a Poisson manifold. We prove that the latter structure can be derived from the BFV-complex by means of homotopy transfer along contractions. Consequently the BFV-complex and the strong homotopy Lie algebroid structure are $L_{\infty}$ quasi-isomorphic and control the same formal deformation problem. However there is a gap between the non-formal information encoded in the BFV-complex and in the strong homotopy Lie algebroid respectively. We prove that there is a one-to-one correspondence between coisotropic submanifolds given by graphs of sections and equivalence classes of normalized Maurer-Cartan elemens of the BFV-complex. This does not hold if one uses the strong homotopy Lie algebroid instead.
dc.description50 pages, 6 figures; version 4 is heavily revised and extended
dc.identifierhttps://arxiv.org/abs/math/0611912
dc.identifierhttp://arxiv.org/abs/math/0611912
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171393
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectSymplectic Geometry
dc.subject18G55; 14D15; 53D17
dc.titleBFV-complex and higher homotopy structures
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