An 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.
On the strong homotopy associative algebra of a foliation
VITAGLIANO, LUCA
2015-01-01
Abstract
An 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
