Partial Dirac structures in infinite dimension

TL;DR

This paper extends the concept of Dirac structures to infinite-dimensional convenient manifolds and Lie algebroids, exploring their properties, limits, and geometric implications.

Contribution

It introduces partial Dirac structures in the infinite-dimensional setting and investigates their classical geometric extensions and limit behaviors.

Findings

Defined partial Dirac structures on convenient Lie algebroids

Extended classical geometric results to infinite dimensions

Analyzed projective and direct limits of these structures

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.