Banach-Lie groupoids and generalized inversion

TL;DR

This paper explores the properties of Banach-Lie groupoids and algebroids, extending classical finite-dimensional results to infinite-dimensional settings and illustrating their application to Banach algebra-related manifolds.

Contribution

It introduces new insights into Banach-Lie groupoids, adapting classical Lie groupoid results to infinite-dimensional contexts and connecting them to Banach algebra manifolds.

Findings

Properties of Banach-Lie groupoids and algebroids established

Locally transitive Banach-Lie groupoids provide new perspectives on infinite-dimensional manifolds

Extension of classical Lie groupoid results to Banach space setting

Abstract

We study a few basic properties of Banach-Lie groupoids and algebroids, adapting some classical results on finite dimensional Lie groupoids. As an illustration of the general theory, we show that the notion of locally transitive Banach-Lie groupoid sheds fresh light on earlier research on some infinite-dimensional manifolds associated with Banach algebras.