Title :

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

Author(s) :

Huebschmann, Johannes [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Banach Center Publications

Pages :

87-102

Publication date :

2000

HAL domain(s) :

Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Algèbres quantiques [math.QA]
Physique [physics]/Physique mathématique [math-ph]
Mathématiques [math]/Physique mathématique [math-ph]

English abstract : [en]

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 ...
Show more >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 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 generator in terms of homological duality for differential graded LR-algebras.Show less >

Language :

Anglais

Popular science :

Non

Comment :

15 pages, no proofs; proofs in expanded version arXiv:math/9811069

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL