Partial Dirac structures in infinite dimension

Abstract

In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenient Lie algebroids and manifolds. We then look for those structures whose classical geometrical results in finite dimension can be extended to this infinite dimensional context. Finally, we are interested in the projective and direct limits of such structures.

2 figures