| | |
| | |
Stat |
Members: 3643 Articles: 2'488'730 Articles rated: 2609
29 March 2024 |
|
| | | |
|
Article overview
| |
|
Twilled Lie-Rinehart algebras and differential Batalin-Vilkovisky algebras | Johannes Huebschmann
; | Date: |
10 Nov 1998 | Subject: | Differential Geometry; Algebraic Geometry MSC-class: 17B55;17B56;17B65;17B66;17B70;17B81;31C16;32G05;53C05;81T70 | math.DG math.AG | Abstract: | Twilled 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. | Source: | arXiv, math.DG/9811069 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |