# Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras

Banach Center Publications (2000)

- Volume: 51, Issue: 1, page 87-102
- ISSN: 0137-6934

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topHuebschmann, Johannes. "Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras." Banach Center Publications 51.1 (2000): 87-102. <http://eudml.org/doc/209047>.

@article{Huebschmann2000,

abstract = {Twilled L(ie-)R(inehart)-algebras 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 (strict) 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-algebra 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 a generator in terms of homological duality for differential graded LR-algebras.},

author = {Huebschmann, Johannes},

journal = {Banach Center Publications},

keywords = {differential graded Lie algebra; twilled Lie-Rinehart algebra; Lie-Rinehart algebra; Batalin-Vilkovisky algebra; Gerstenhaber algebra; mirror conjecture; Calabi-Yau manifold; Lie bialgebra; almost complex manifold},

language = {eng},

number = {1},

pages = {87-102},

title = {Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras},

url = {http://eudml.org/doc/209047},

volume = {51},

year = {2000},

}

TY - JOUR

AU - Huebschmann, Johannes

TI - Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras

JO - Banach Center Publications

PY - 2000

VL - 51

IS - 1

SP - 87

EP - 102

AB - Twilled L(ie-)R(inehart)-algebras 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 (strict) 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-algebra 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 a generator in terms of homological duality for differential graded LR-algebras.

LA - eng

KW - differential graded Lie algebra; twilled Lie-Rinehart algebra; Lie-Rinehart algebra; Batalin-Vilkovisky algebra; Gerstenhaber algebra; mirror conjecture; Calabi-Yau manifold; Lie bialgebra; almost complex manifold

UR - http://eudml.org/doc/209047

ER -

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