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EnglishAn involutive distribution C on a smooth manifold M is a Lie-algebroid acting on sections of the normal bundle TM/C. It is known that the Chevalley-Eilenberg complex associated to this representation of C possesses the structure X of a strong homotopy Lie-Rinehart algebra. It is natural to interpret X as the (derived) Lie-Rinehart algebra of vector fields on the space P of integral manifolds of C. In this paper, I show that X is embedded in a strong homotopy associative algebra D of (normal) differential operators. It is natural to interpret D as the (derived) associative algebra of differential operators on P. Finally, I speculate about the interpretation of D as the universal enveloping strong homotopy algebra of X.
| Titolo: | On the strong homotopy associative algebra of a foliation |
| Autori: | |
| Data di pubblicazione: | 2015 |
| Rivista: | |
| Handle: | http://hdl.handle.net/11386/4358054 |
| Appare nelle tipologie: | 1.1.2 Articolo su rivista con ISSN |
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