- Tytuł:
- Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras
- Autorzy:
- Huebschmann, Johannes
- Powiązania:
- https://bibliotekanauki.pl/articles/1207674.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
differential graded Lie algebra
twilled Lie-Rinehart algebra
Lie-Rinehart algebra
Batalin-Vilkovisky algebra
Gerstenhaber algebra
mirror conjecture
Calabi-Yau manifold
Lie bialgebra - Opis:
- 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.
- Źródło:
-
Banach Center Publications; 2000, 51, 1; 87-102
0137-6934 - Pojawia się w:
- Banach Center Publications
- Dostawca treści:
- Biblioteka Nauki
Artykuł