Twilled Lie-Rinehart algebras and differential Batalin-Vilkovisky algebras

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dc.creatorHuebschmann, Johannes
dc.date1998-11-10
dc.date.accessioned2026-07-07T05:26:49Z
dc.date.available2026-07-07T05:26:49Z
dc.descriptionTwilled L(ie)-R(inehart) algebas generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an almost twilled pre-LR algebra, which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR-structures in terms of certain associated differential (bi)graded Lie and G(erstenhaber)-algebras; in particular, the G-algebra arising from an almost complex structure is a d(ifferential) G-algebra iff the almost complex structure is integrable. Such G-algebras, endowed with a generator turning them into a B(atalin)-V(ilkovisky) algebra, occur on the B-side of the mirror conjecture. We generalize a result of Koszul to those dG-algebras which arise from twilled LR-algebras. A special case thereof explains the relationship between holomorphic volume forms and exact generators for the corresponding dG-algebras and thus yields in particular a conceptual proof of the Tian-Todorov lemma. We give a differential homological algebra interpretation for twilled LR-algebras and by means of it we elucidate the notion of generator in terms of homological duality for differential graded LR-algebras. Finally we indicate how some of our results might be globalized by means of Lie groupoids.
dc.description54 pages, AMSTeX 2.1
dc.identifierhttps://arxiv.org/abs/math/9811069
dc.identifierhttp://arxiv.org/abs/math/9811069
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77694
dc.subjectDifferential Geometry
dc.subjectAlgebraic Geometry
dc.subject17B55;17B56;17B65;17B66;17B70;17B81;31C16;32G05;53C05;81T70
dc.titleTwilled Lie-Rinehart algebras and differential Batalin-Vilkovisky algebras
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